Sesión 07

Diseño de Bloques Incompletos


Christian Vásquez-Velasco, Bach., M.Sc.(c)

InkaStats Academy

2023

Diseño de Bloques incompletos Balanceados


Planeamiento


Instalar paquetes necesarios


# install.packages("devtools")
# devtools::install_github("emitanaka/edibble", force = T)
# devtools::install_github("emitanaka/deggust", force = T)

if (!require("pacman")) install.packages("pacman")
pacman::p_load(readxl, agricolae, agricolaeplotr, car, tidyverse, PMCMRplus, outliers, nortest, mvtnorm, lmtest, ExpDes, edibble, gt,
               gtsummary, devtools, deggust, xlsx, desplot,
               ggResidpanel, fastGraph, gvlma)
package 'xlsx' successfully unpacked and MD5 sums checked

The downloaded binary packages are in
    C:\Users\cvasquezv\AppData\Local\Temp\RtmpeMxeS3\downloaded_packages

Crear un libro con el paquete agricolae


variedades <- c("Amazon", "Coari x Lame", "Coari x Yangambí",
                "Unipalma")

k <- length(variedades)-1

salida <- agricolae::design.bib(trt = variedades,
                                k = k,
                                serie = 2,
                                seed = 123,
                                kinds = "Mersenne-Twister",
                                randomization = TRUE)

Parameters BIB
==============
Lambda     : 2
treatmeans : 4
Block size : 3
Blocks     : 4
Replication: 3 

Efficiency factor 0.8888889 

<<< Book >>>

Eficiencia del diseño

salida$statistics
       lambda treatmeans blockSize blocks r Efficiency
values      2          4         3      4 3  0.8888889

Del resultado se observa que:

  • Lambda = 2, significa que cada par de tratamientos será evaluado 2 veces en un semi bloque.

  • Blocks = 4, significa que tenemos 4 semibloques.

  • BlockSize = 3, significa que en cada semibloque tendrá 3 columnas.

  • r = 3, significa que cada tratamiento se repite 3 veces en el diseño.

  • Efficiency = 88.9 %, sugiere que con 3 repeticiones por tratamiento la eficiencia del diseño alcanza el 88.9 %.

Sketch del diseño

salida$sketch
     [,1]               [,2]               [,3]          
[1,] "Coari x Yangambí" "Coari x Lame"     "Unipalma"    
[2,] "Amazon"           "Coari x Yangambí" "Coari x Lame"
[3,] "Unipalma"         "Coari x Lame"     "Amazon"      
[4,] "Coari x Yangambí" "Unipalma"         "Amazon"      
salida$book %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Sketch codificado del diseño

print(matrix(salida$book[,1], byrow=TRUE, ncol=3))
     [,1] [,2] [,3]
[1,]  101  102  103
[2,]  201  202  203
[3,]  301  302  303
[4,]  401  402  403

Guardar el libro generado

write.table(salida$book, "books/bib.txt",
            row.names = FALSE, sep = "\t")

write.xlsx(salida$book, "books/bib.xlsx", sheetName = "book", append = FALSE, row.names = FALSE)

Libro de campo

fieldbook <- salida %>% 
  zigzag()

fieldbook %>%
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro de campo generado

write.table(fieldbook,
  "books/bib.txt",
  row.names = FALSE, sep = "\t")

write.xlsx(fieldbook,
  "books/bib.xlsx",
  sheetName = "book",
  append = FALSE,
  row.names = FALSE)
agricolaeplotr::plot_bib(design = salida,
                          factor_name = "variedades",
                          reverse_y = TRUE,
                          reverse_x = FALSE) +
  labs(fill = "Variedades",
       x = "Columnas",
       y = "Filas")

Crear un libro de campo con el paquete edibble


menu_bibd()
design("Balanced Incomplete Block Design") %>%
  set_units(block = 8,
            unit = nested_in(block, 2)) %>%
  set_trts(trt = 4) %>%
  allot_trts(trt ~ unit) %>%
  assign_trts("random", seed = 424) %>%
  serve_table()
bib <- takeout(menu_bibd(t = 4, r = 3, k = k, seed = 123))
bib %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
bib2 <- design("Randomised Complete Block Design") %>%
  set_units(block = 4,
            unit = nested_in(block, 3)) %>%
  set_trts(variedades = c("Amazon", "Coari x Lame", "Coari x Yangambí", "Unipalma")) %>%
  allot_trts(variedades ~ unit) %>%
  assign_trts("random", seed = 123) %>%
  serve_table()
bib2 %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
deggust::autoplot(bib2)
plot(bib2)

Análisis del diseño


Importación de datos


archivos <- list.files(pattern = "data bib.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "ej1")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(run = as.factor(run),
         psi = as.factor(psi))
attach(data)

Creación del modelo lineal


modelo.bib <- lm(monovinyl ~ psi + run , data = data)

Definición del modelo


\[Y_i = \beta_0 + \beta_1*Psi_{325} + \beta_2*Psi_{400} + \beta_3*Psi_{475} + \beta_4**Psi_{550} + \beta_5*B_{II} + \beta_6*B_{III} + \beta_7*B_{IV} + \beta_8*B_{V} + \beta_9*B_{VI} + \beta_10*B_{VII} + \beta_11*B_{VIII} + \beta_12*B_{IX} + \beta_13*B_{X} + \epsilon\]

\[\hat{Y}_i = \beta_0 + \beta_1*Psi_{325} + \beta_2*Psi_{400} + \beta_3*Psi_{475} + \beta_4**Psi_{550} + \beta_5*B_{II} + \beta_6*B_{III} + \beta_7*B_{IV} + \beta_8*B_{V} + \beta_9*B_{VI} + \beta_10*B_{VII} + \beta_11*B_{VIII} + \beta_12*B_{IX} + \beta_13*B_{X} + \beta_8*B_{V}\]

summary(modelo.bib)

Call:
lm(formula = monovinyl ~ psi + run, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.7556 -2.7944 -0.7667  3.4444  7.4444 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  16.8667     3.7936   4.446 0.000406 ***
psi325       -2.9333     3.5122  -0.835 0.415912    
psi400       10.4000     3.5122   2.961 0.009195 ** 
psi475       18.3333     3.5122   5.220 8.42e-05 ***
psi550       30.2000     3.5122   8.599 2.15e-07 ***
run10         5.2000     4.6829   1.110 0.283230    
run2          3.6222     4.6829   0.773 0.450508    
run3         12.5778     4.8271   2.606 0.019119 *  
run4          0.4889     4.8271   0.101 0.920586    
run5          5.9333     4.6829   1.267 0.223284    
run6          1.5556     4.6829   0.332 0.744069    
run7          0.6444     4.6829   0.138 0.892261    
run8          3.9333     4.8271   0.815 0.427121    
run9          2.0444     4.6829   0.437 0.668255    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.553 on 16 degrees of freedom
Multiple R-squared:  0.9115,    Adjusted R-squared:  0.8396 
F-statistic: 12.68 on 13 and 16 DF,  p-value: 4.768e-06

Verificación visual de los supuestos del modelo


performance::check_model(modelo.bib)
ggResidpanel::resid_panel(modelo.bib)
influence.measures(modelo.bib)
Influence measures of
     lm(formula = monovinyl ~ psi + run, data = data) :

     dfb.1_  dfb.p325  dfb.p400  dfb.p475  dfb.p550  dfb.rn10  dfb.run2
1  -0.19383  8.97e-02  5.98e-02  8.97e-02  5.98e-02  9.72e-02  1.20e-01
2   0.53609  4.34e-01  1.45e-01 -9.79e-16  1.45e-01 -5.79e-01 -4.70e-01
3  -0.41655 -1.60e-16 -1.12e-01 -3.37e-01 -1.12e-01  4.50e-01  4.50e-01
4  -0.07950  1.03e-01  1.03e-01  1.55e-01  1.55e-01 -2.58e-02 -2.06e-01
5  -0.34047  2.76e-01  2.76e-01  8.27e-01  3.17e-16 -6.90e-02  1.10e+00
6   0.06460 -2.09e-01 -2.09e-01 -2.61e-16 -6.28e-01  5.23e-02 -6.80e-01
7   0.01088 -3.52e-02  1.76e-02 -2.02e-17  1.76e-02 -4.41e-03 -1.32e-02
8  -0.00899  2.91e-02 -5.83e-02  2.12e-17  2.91e-02  1.46e-02  3.03e-17
9   0.01447 -4.69e-02 -4.69e-02 -9.76e-18  9.38e-02  1.17e-02 -3.52e-02
10 -0.07902 -2.19e-16 -5.12e-01  2.56e-01  2.56e-01  1.28e-01 -6.40e-02
11  0.01467 -2.14e-17  2.38e-02 -4.75e-02  2.38e-02 -5.94e-03 -5.94e-03
12  0.08911  1.92e-16 -2.89e-01 -2.89e-01  5.77e-01  7.22e-02 -1.44e-01
13  0.00923 -5.98e-02 -2.79e-17  2.99e-02  2.99e-02  2.99e-17 -2.24e-02
14 -0.06692 -2.17e-01 -2.34e-16  4.34e-01 -2.17e-01  2.33e-16 -4.29e-17
15 -0.11179  1.81e-01 -2.67e-17  1.81e-01 -3.62e-01 -8.61e-17  1.36e-01
16  0.08429 -1.09e-01 -1.64e-01 -1.64e-01 -1.09e-01  4.10e-02  4.53e-17
17 -0.04598  1.49e-01  4.47e-01  6.20e-17  1.49e-01 -1.12e-01 -1.11e-17
18  0.26187 -2.12e-01  4.16e-17 -6.36e-01 -2.12e-01  2.43e-16  4.59e-16
19 -0.24972  4.86e-01  4.86e-01  3.24e-01  3.24e-01 -1.21e-01  4.05e-02
20  0.06744 -1.64e-01 -5.90e-17 -5.46e-02 -5.46e-02  1.29e-16 -2.73e-02
21 -0.06986  2.80e-16  6.79e-01  2.26e-01  2.26e-01 -1.70e-01 -5.66e-02
22  0.00851 -1.38e-02 -2.07e-02 -1.38e-02 -2.07e-02  5.17e-03  1.72e-03
23  0.02559 -4.15e-02 -1.24e-01 -4.15e-02 -2.44e-17  3.11e-02 -1.04e-02
24 -0.02131  3.45e-02  2.88e-17  3.45e-02  1.04e-01 -2.32e-17 -1.73e-02
25  0.28498 -5.54e-01 -3.69e-01 -3.69e-01 -5.54e-01  9.23e-02  1.67e-16
26  0.27353 -6.65e-01 -2.22e-01 -2.22e-01 -3.03e-16  5.54e-02 -1.66e-01
27 -0.00947  2.48e-17  3.07e-02  3.07e-02  9.20e-02 -7.67e-03 -2.30e-02
28 -0.05425  3.52e-01 -1.76e-01 -1.76e-01  1.69e-16  7.03e-01  8.79e-02
29 -0.03132  5.07e-02 -1.01e-01  5.07e-02  3.51e-17 -1.65e-01  1.27e-02
30  0.03698  1.20e-01  1.20e-01 -2.40e-01  6.75e-17 -4.79e-01  3.00e-02
    dfb.run3  dfb.run4  dfb.run5  dfb.run6  dfb.run7  dfb.run8  dfb.run9
1   1.02e-01  1.02e-01  9.72e-02  1.20e-01  1.20e-01  1.23e-01  1.20e-01
2  -5.97e-01 -4.92e-01 -5.79e-01 -4.70e-01 -5.79e-01 -4.92e-01 -5.79e-01
3   3.82e-01  4.64e-01  4.50e-01  4.50e-01  3.66e-01  3.82e-01  3.66e-01
4  -2.50e-02 -3.75e-02 -3.86e-02 -5.00e-17  1.29e-02 -5.41e-17 -5.43e-17
5   1.34e-01 -1.55e-16 -4.04e-16 -2.46e-16  1.38e-01  2.01e-01  2.07e-01
6   2.03e-01  1.52e-01  1.57e-01  5.49e-16  5.23e-02  1.52e-01  1.57e-01
7  -7.27e-02 -1.71e-02 -4.41e-03 -1.32e-02 -4.41e-03 -1.71e-02 -4.41e-03
8  -9.89e-02  1.41e-02 -7.28e-03  2.19e-02  1.46e-02  1.41e-02 -7.28e-03
9   1.59e-01 -2.27e-02 -2.34e-02  2.40e-17  1.17e-02 -2.27e-02 -2.34e-02
10  1.24e-01 -8.69e-01 -6.40e-02  1.28e-01  1.92e-01  1.24e-01  2.02e-16
11 -2.31e-02 -9.80e-02 -5.94e-03 -5.94e-03 -1.78e-02 -2.31e-02 -1.78e-02
12 -1.40e-01  9.80e-01 -1.44e-01  7.22e-02  2.86e-16 -1.40e-01 -2.17e-01
13  3.70e-17 -2.18e-02 -1.20e-01 -1.50e-02  7.48e-03 -1.45e-02  3.94e-17
14  1.58e-01  1.93e-16  8.67e-01 -5.42e-02  1.08e-01  1.05e-01  1.63e-01
15  1.32e-01  1.32e-01 -5.89e-01  4.53e-02  4.53e-02  1.76e-01  1.36e-01
16  2.65e-02  3.97e-02  2.73e-02  2.19e-01  6.10e-17  3.85e-17 -1.37e-02
17 -1.45e-01 -1.08e-01 -3.72e-02  4.84e-01 -1.12e-01 -1.08e-01 -3.72e-02
18 -1.03e-01  3.65e-16  5.30e-02 -8.49e-01 -1.59e-01 -1.54e-01 -1.06e-01
19 -1.18e-01 -7.85e-02 -8.09e-02 -3.06e-16 -6.47e-01 -2.45e-16 -2.98e-16
20  1.36e-16 -2.65e-02  1.37e-02 -4.10e-02 -2.19e-01 -3.97e-02  1.29e-16
21 -1.65e-01 -2.20e-01 -5.66e-02 -1.70e-01  7.36e-01 -1.65e-01  1.79e-16
22  6.69e-03  6.69e-03  5.17e-03  1.72e-03  1.72e-03  2.84e-02  1.72e-03
23  2.01e-02  2.01e-02  4.06e-17  2.07e-02  2.07e-02 -1.41e-01 -1.04e-02
24 -1.67e-02 -1.67e-02 -2.59e-02  8.63e-03  8.63e-03  1.17e-01 -1.73e-02
25  1.34e-01  8.96e-02  1.39e-01 -4.62e-02  2.16e-16  1.67e-16  7.39e-01
26  4.14e-16 -1.07e-01  3.24e-16 -1.11e-01  3.32e-16 -1.61e-01 -8.86e-01
27 -2.23e-02 -2.98e-02 -2.30e-02 -7.67e-03  1.31e-17 -2.23e-02  9.97e-02
28 -5.11e-17  1.28e-01 -4.13e-17  1.32e-01 -1.41e-17  8.53e-02 -4.40e-02
29  3.69e-02  3.69e-02 -7.03e-17  3.81e-02  3.81e-02  4.92e-02  1.27e-02
30 -8.72e-02  5.01e-17  6.02e-17  5.66e-17 -8.99e-02 -5.81e-02 -5.99e-02
     dffit cov.r   cook.d   hat inf
1  -0.1938 4.447 0.002854 0.467   *
2   0.9382 1.865 0.062843 0.467    
3  -0.7290 2.655 0.038912 0.467    
4  -0.3339 4.111 0.008424 0.467   *
5   1.7875 0.219 0.195777 0.467   *
6  -1.3566 0.737 0.122981 0.467    
7  -0.1142 4.564 0.000993 0.467   *
8  -0.1888 4.456 0.002710 0.467   *
9   0.3038 4.196 0.006983 0.467   *
10 -1.6594 0.322 0.173422 0.467    
11 -0.1540 4.513 0.001803 0.467   *
12  1.8712 0.169 0.210595 0.467    
13 -0.1938 4.447 0.002854 0.467   *
14  1.4053 0.650 0.130787 0.467    
15 -1.1738 1.144 0.095000 0.467    
16  0.3540 4.051 0.009460 0.467   *
17  0.9656 1.771 0.066324 0.467    
18 -1.3748 0.704 0.125880 0.467    
19 -1.0488 1.500 0.077330 0.467    
20 -0.3540 4.051 0.009460 0.467   *
21  1.4671 0.552 0.140883 0.467    
22  0.0447 4.618 0.000152 0.467   *
23 -0.2687 4.286 0.005472 0.467   *
24  0.2238 4.388 0.003800 0.467   *
25  1.1969 1.085 0.098408 0.467    
26 -1.4361 0.600 0.135788 0.467    
27  0.1988 4.437 0.003002 0.467   *
28  1.1393 1.236 0.090001 0.467    
29 -0.3289 4.126 0.008174 0.467   *
30 -0.7766 2.468 0.043928 0.467    
influenceIndexPlot(modelo.bib)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.bib,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.28811325      2.551276  0.9964
   2     -0.27182790      2.480829  0.5188
   3      0.13016574      1.608089  0.4964
   4      0.09606377      1.670199  0.9740
   5     -0.08506275      1.855617  0.4348
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.bib, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.bib
DW = 2.5513, p-value = 0.9991
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que existe suficiente evidencia estadística para no rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.bib))

    Shapiro-Wilk normality test

data:  rstudent(modelo.bib)
W = 0.95758, p-value = 0.2683
ad.test(rstudent(modelo.bib))

    Anderson-Darling normality test

data:  rstudent(modelo.bib)
A = 0.43833, p-value = 0.2754
lillie.test(rstudent(modelo.bib))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.bib)
D = 0.11542, p-value = 0.3898
ks.test(rstudent(modelo.bib), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.bib)
D = 0.11525, p-value = 0.7784
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.bib))

    Cramer-von Mises normality test

data:  rstudent(modelo.bib)
W = 0.073513, p-value = 0.2426
pearson.test(rstudent(modelo.bib))

    Pearson chi-square normality test

data:  rstudent(modelo.bib)
P = 4.6667, p-value = 0.4579
sf.test(rstudent(modelo.bib))

    Shapiro-Francia normality test

data:  rstudent(modelo.bib)
W = 0.96808, p-value = 0.4141

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento.

ncvTest(modelo.bib)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.2717253, Df = 1, p = 0.60218
bptest(modelo.bib)

    studentized Breusch-Pagan test

data:  modelo.bib
BP = 12.771, df = 13, p-value = 0.4656
bptest(modelo.bib, studentize = F)

    Breusch-Pagan test

data:  modelo.bib
BP = 6.9179, df = 13, p-value = 0.9063
olsrr::ols_test_breusch_pagan(modelo.bib)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

                Data                  
 -------------------------------------
 Response : monovinyl 
 Variables: fitted values of monovinyl 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    0.2717253 
 Prob > Chi2   =    0.6021768 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.bib %>% gvlma()

Call:
lm(formula = monovinyl ~ psi + run, data = data)

Coefficients:
(Intercept)       psi325       psi400       psi475       psi550        run10  
    16.8667      -2.9333      10.4000      18.3333      30.2000       5.2000  
       run2         run3         run4         run5         run6         run7  
     3.6222      12.5778       0.4889       5.9333       1.5556       0.6444  
       run8         run9  
     3.9333       2.0444  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                     Value p-value                Decision
Global Stat        1.38657  0.8465 Assumptions acceptable.
Skewness           0.20516  0.6506 Assumptions acceptable.
Kurtosis           1.05028  0.3054 Assumptions acceptable.
Link Function      0.08780  0.7670 Assumptions acceptable.
Heteroscedasticity 0.04332  0.8351 Assumptions acceptable.

Análisis de varianza

\[Y = \mu + \tau_{i} + \beta_{j} + \epsilon_{ij}\]

\[\hat{Y} = \mu + \tau_{i} + \beta_{j}\]

Para los tratamientos:

\(H_0: \tau_{A} = \tau_{B} = \tau_{C} = \tau_{D} = \tau_{E} = 0\)

\(H_1: \text{En al menos un tratamiento el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un tratamiento.}\)

Para los bloques:

\(H_0: \beta_{I} = \beta_{II} = \beta_{III} = ... = \beta_{X} = 0\)

\(H_1: \text{En al menos un bloque el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un bloque.}\)

Comparaciones de medias

  • A vs B:

\(H_0: \mu_{A} - \mu_{B} = 0\)

\(H_1: \mu_{A} - \mu_{B} \neq 0\)

  • A vs C:

\(H_0: \mu_{A} - \mu_{C} = 0\)

\(H_1: \mu_{A} - \mu_{C} \neq 0\)

  • A vs D:

\(H_0: \mu_{A} - \mu_{D} = 0\)

\(H_1: \mu_{A} - \mu_{D} \neq 0\)

  • A vs E:

\(H_0: \mu_{A} - \mu_{E} = 0\)

\(H_1: \mu_{A} - \mu_{E} \neq 0\)

  • B vs C:

\(H_0: \mu_{B} - \mu_{C} = 0\)

\(H_1: \mu_{B} - \mu_{C} \neq 0\)

  • B vs D:

\(H_0: \mu_{B} - \mu_{D} = 0\)

\(H_1: \mu_{B} - \mu_{D} \neq 0\)

  • B vs E:

\(H_0: \mu_{B} - \mu_{E} = 0\)

\(H_1: \mu_{B} - \mu_{E} \neq 0\)

  • C vs D:

\(H_0: \mu_{C} - \mu_{D} = 0\)

\(H_1: \mu_{C} - \mu_{D} \neq 0\)

  • C vs E:

\(H_0: \mu_{C} - \mu_{E} = 0\)

\(H_1: \mu_{C} - \mu_{E} \neq 0\)

  • D vs E:

\(H_0: \mu_{D} - \mu_{E} = 0\)

\(H_1: \mu_{D} - \mu_{E} \neq 0\)

data <- data%>%
  dplyr::mutate(response = monovinyl)
attach(data)
agricolae::BIB.test(trt = psi,
                    block = run,
                    y = response,
                    console = TRUE,
                    test = "lsd") -> anova.bib

ANALYSIS BIB:  response 
Class level information

Block:  1 2 3 4 5 6 7 8 9 10
Trt  :  250 325 475 550 400

Number of observations:  30 

Analysis of Variance Table

Response: response
            Df Sum Sq Mean Sq F value    Pr(>F)    
block.unadj  9 1394.7  154.96  5.0249  0.002529 ** 
trt.adj      4 3688.6  922.14 29.9020 3.026e-07 ***
Residuals   16  493.4   30.84                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

coefficient of variation: 17.5 %
response Means: 31.66667 

psi,  statistics

    response mean.adj       SE r      std Min Max
250 18.83333 20.46667 2.441759 6 3.868678  13  24
325 18.33333 17.53333 2.441759 6 6.153590  10  26
400 31.33333 30.86667 2.441759 6 5.955390  21  39
475 38.00000 38.80000 2.441759 6 6.928203  31  47
550 51.83333 50.66667 2.441759 6 5.636193  45  61

LSD test
Std.diff   : 3.512201
Alpha      : 0.05
LSD        : 7.445533
Parameters BIB
Lambda     : 3
treatmeans : 5
Block size : 3
Blocks     : 10
Replication: 6 

Efficiency factor 0.8333333 

<<< Book >>>

Comparison between treatments means
          Difference pvalue sig.
250 - 325   2.933333 0.4160     
250 - 400 -10.400000 0.0092   **
250 - 475 -18.333333 0.0000  ***
250 - 550 -30.200000 0.0000  ***
325 - 400 -13.333333 0.0016   **
325 - 475 -21.266667 0.0000  ***
325 - 550 -33.133333 0.0000  ***
400 - 475  -7.933333 0.0382    *
400 - 550 -19.800000 0.0000  ***
475 - 550 -11.866667 0.0038   **

Treatments with the same letter are not significantly different.

    response groups
550 50.66667      a
475 38.80000      b
400 30.86667      c
250 20.46667      d
325 17.53333      d
power.anova.test(groups = 5,
                 n = 10,
                 between.var = anova(modelo.bib)[2,2], 
                 within.var = deviance(modelo.bib),
                 sig.level = 0.05)

     Balanced one-way analysis of variance power calculation 

         groups = 5
              n = 10
    between.var = 346.9111
     within.var = 493.4222
      sig.level = 0.05
          power = 0.9900861

NOTE: n is number in each group

Conclusión. A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un tratamiento (psi) tiene un efecto sobre el monovinyl estadísticamente diferente del resto de tratamientos.

plot(anova.bib)

Warning  values plot is not adjusted

Diseño de Bloques Parcialmente Balanceados


Diseño Lattice


Planeamiento


Crear un libro con el paquete agricolae


genotipos <- LETTERS[1:9]

r <- 3

salida <- agricolae::design.lattice(
  trt = genotipos,
  r = r,
  serie = 2,
  seed = 123,
  kinds = "Mersenne-Twister",
  randomization = TRUE)

Lattice design,  triple   3 x 3 

Efficiency factor
(E ) 0.7272727 

<<< Book >>>

Eficiencia del diseño

salida$statistics
       treatmens blockSize blocks Efficiency
values         9         3      3  0.7272727

Del resultado se observa que:

  • Tratamientos = 9.

  • Blocks = 3, significa que tenemos 3 semibloques.

  • BlockSize = 3, significa que en cada tratamiento tendrá 3 semibloques.

  • Efficiency = 72.7 %, sugiere que con 3 bloques por tratamiento la eficiencia del diseño alcanza el 72.7 %.

Sketch del diseño

salida$sketch
$rep1
     [,1] [,2] [,3]
[1,] "C"  "F"  "I" 
[2,] "B"  "H"  "E" 
[3,] "G"  "A"  "D" 

$rep2
     [,1] [,2] [,3]
[1,] "F"  "H"  "A" 
[2,] "C"  "B"  "G" 
[3,] "I"  "E"  "D" 

$rep3
     [,1] [,2] [,3]
[1,] "F"  "E"  "G" 
[2,] "I"  "B"  "A" 
[3,] "C"  "H"  "D" 
salida$book %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Sketch codificado del diseño

print(matrix(salida$book[,1], byrow=TRUE, ncol=3))
      [,1] [,2] [,3]
 [1,]  101  102  103
 [2,]  104  105  106
 [3,]  107  108  109
 [4,]  201  202  203
 [5,]  204  205  206
 [6,]  207  208  209
 [7,]  301  302  303
 [8,]  304  305  306
 [9,]  307  308  309

Guardar el libro generado

write.table(salida$book, "books/lattice.txt",
            row.names = FALSE, sep = "\t")

write.xlsx(salida$book, "books/lattice.xlsx", sheetName = "book", append = FALSE, row.names = FALSE)

Libro de campo

fieldbook <- salida %>% 
  zigzag()

fieldbook %>%
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro de campo generado

write.table(fieldbook,
  "books/lattice.txt",
  row.names = FALSE, sep = "\t")

write.xlsx(fieldbook,
  "books/lattice.xlsx",
  sheetName = "book",
  append = FALSE,
  row.names = FALSE)
agricolaeplotr::plot_lattice_triple(design = salida,
                          factor_name = "trt",
                          reverse_y = FALSE,
                          reverse_x = TRUE) +
  labs(fill = "genotipos",
       x = "Columnas",
       y = "Filas")

Diseño Alpha


Planeamiento


Crear un libro con el paquete agricolae


genotipos <- LETTERS[1:12]

r <- 3
k <- 3

salida <- agricolae::design.alpha(
  trt = genotipos,
  r = r,
  k = k,
  serie = 2,
  seed = 123,
  kinds = "Mersenne-Twister",
  randomization = TRUE)

Alpha Design (0,1) - Serie  III 

Parameters Alpha Design
=======================
Treatmeans : 12
Block size : 3
Blocks     : 4
Replication: 3 

Efficiency factor
(E ) 0.7096774 

<<< Book >>>

Eficiencia del diseño

salida$statistics
       treatments blocks Efficiency
values         12      4  0.7096774

Del resultado se observa que:

  • Tratamientos = 12.

  • Blocks = 4, significa que tenemos 4 semibloques.

  • BlockSize = 3, significa que en cada semibloque tendrá 3 columnas.

  • Efficiency = 70.96 %, sugiere que con 3 bloques por tratamiento la eficiencia del diseño alcanza el 70.96 %.

Sketch del diseño

salida$sketch
$rep1
     [,1] [,2] [,3]
[1,] "A"  "I"  "G" 
[2,] "J"  "K"  "C" 
[3,] "F"  "E"  "D" 
[4,] "L"  "B"  "H" 

$rep2
     [,1] [,2] [,3]
[1,] "L"  "D"  "C" 
[2,] "H"  "A"  "E" 
[3,] "F"  "K"  "I" 
[4,] "J"  "G"  "B" 

$rep3
     [,1] [,2] [,3]
[1,] "D"  "A"  "K" 
[2,] "F"  "L"  "J" 
[3,] "I"  "B"  "E" 
[4,] "C"  "G"  "H" 
salida$book %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Sketch codificado del diseño

print(matrix(salida$book[,1], byrow=TRUE, ncol=3))
      [,1] [,2] [,3]
 [1,]  101  102  103
 [2,]  104  105  106
 [3,]  107  108  109
 [4,]  110  111  112
 [5,]  201  202  203
 [6,]  204  205  206
 [7,]  207  208  209
 [8,]  210  211  212
 [9,]  301  302  303
[10,]  304  305  306
[11,]  307  308  309
[12,]  310  311  312

Guardar el libro generado

write.table(salida$book, "books/alpha.txt",
            row.names = FALSE, sep = "\t")

write.xlsx(salida$book, "books/alpha.xlsx", sheetName = "book", append = FALSE, row.names = FALSE)

Libro de campo

fieldbook <- salida %>% 
  zigzag()

fieldbook %>%
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro de campo generado

write.table(fieldbook,
  "books/alpha.txt",
  row.names = FALSE, sep = "\t")

write.xlsx(fieldbook,
  "books/alpha.xlsx",
  sheetName = "book",
  append = FALSE,
  row.names = FALSE)
agricolaeplotr::plot_alpha(design = salida,
                          factor_name = "genotipos",
                          x = "cols",
                          y = "block",
                          reverse_y = TRUE,
                          reverse_x = FALSE) +
  labs(fill = "genotipos",
       x = "Columnas",
       y = "Filas")

Diseño Cíclico


Planeamiento


Crear un libro con el paquete agricolae


genotipos <- LETTERS[1:8]

r <- 6
k <- 2

salida <- agricolae::design.cyclic(
  trt = genotipos,
  r = r,
  k = k,
  serie = 2,
  seed = 123,
  kinds = "Mersenne-Twister",
  randomization = TRUE)

cyclic design
Generator block basic:
1 2 
1 4 
1 3 

Parameters
===================
treatmeans : 8
Block size : 2
Replication: 6 

Eficiencia del diseño

Del resultado se observa que:

  • Tratamientos = 8.

  • Blocks = 4, significa que tenemos 4 semibloques.

  • BlockSize = 2, significa que en cada semibloque tendrá 2 columnas.

  • Replication = 6, significa que en cada tratamiento tendrá 6 repeticiones.

Sketch del diseño

salida$sketch[1]
[[1]]
     [,1] [,2]
[1,] "A"  "H" 
[2,] "E"  "F" 
[3,] "C"  "D" 
[4,] "G"  "F" 
[5,] "A"  "B" 
[6,] "E"  "D" 
[7,] "H"  "G" 
[8,] "B"  "C" 
salida$sketch[2]
[[1]]
     [,1] [,2]
[1,] "C"  "H" 
[2,] "E"  "B" 
[3,] "H"  "E" 
[4,] "A"  "D" 
[5,] "F"  "A" 
[6,] "G"  "B" 
[7,] "G"  "D" 
[8,] "F"  "C" 
salida$sketch[3]
[[1]]
     [,1] [,2]
[1,] "C"  "A" 
[2,] "H"  "B" 
[3,] "C"  "E" 
[4,] "A"  "G" 
[5,] "B"  "D" 
[6,] "G"  "E" 
[7,] "F"  "H" 
[8,] "F"  "D" 
salida$book %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Sketch codificado del diseño

print(matrix(salida$book[,1], byrow=TRUE, ncol=2))
      [,1] [,2]
 [1,]  101  102
 [2,]  103  104
 [3,]  105  106
 [4,]  107  108
 [5,]  109  110
 [6,]  111  112
 [7,]  113  114
 [8,]  115  116
 [9,]  201  202
[10,]  203  204
[11,]  205  206
[12,]  207  208
[13,]  209  210
[14,]  211  212
[15,]  213  214
[16,]  215  216
[17,]  301  302
[18,]  303  304
[19,]  305  306
[20,]  307  308
[21,]  309  310
[22,]  311  312
[23,]  313  314
[24,]  315  316

Guardar el libro generado

write.table(salida$book, "books/cyclic.txt",
            row.names = FALSE, sep = "\t")

write.xlsx(salida$book, "books/cyclic.xlsx", sheetName = "book", append = FALSE, row.names = FALSE)

Libro de campo

fieldbook <- salida %>% 
  zigzag()

fieldbook %>%
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro de campo generado

write.table(fieldbook,
  "books/cyclic.txt",
  row.names = FALSE, sep = "\t")

write.xlsx(fieldbook,
  "books/cyclic.xlsx",
  sheetName = "book",
  append = FALSE,
  row.names = FALSE)
agricolaeplotr::plot_cyclic(design = salida,
                          factor_name = "genotipos",
                          y = "block",
                          reverse_y = TRUE,
                          reverse_x = FALSE) +
  labs(fill = "genotipos",
       x = "Columnas",
       y = "Filas")

Análisis de Bloques Incompletos Parcialmente Balanceados

Diseño alpha

# alpha design 
Genotype<-c(paste("gen0",1:9,sep=""),paste("gen",10:30,sep=""))
ntr<-length(Genotype)
r<-2
k<-3
s<-10
obs<-ntr*r
b <- s*r
book<-design.alpha(Genotype,k,r,seed=5)

Alpha Design (0,1) - Serie  I 

Parameters Alpha Design
=======================
Treatmeans : 30
Block size : 3
Blocks     : 10
Replication: 2 

Efficiency factor
(E ) 0.6170213 

<<< Book >>>
book$book[,3]<- gl(20,3)
dbook<-book$book
# dataset
yield<-c(5,2,7,6,4,9,7,6,7,9,6,2,1,1,3,2,4,6,7,9,8,7,6,4,3,2,2,1,1,2,
     1,1,2,4,5,6,7,8,6,5,4,3,1,1,2,5,4,2,7,6,6,5,6,4,5,7,6,5,5,4)
rm(Genotype)
model <- with(dbook,PBIB.test(block, Genotype, replication, yield, k=3, method="ML"))

<<< to see the objects: means, comparison and groups. >>>
model$ANOVA
Analysis of Variance Table

Response: yield
          Df Sum Sq Mean Sq F value Pr(>F)
Genotype  29 32.669  1.1265  2.0066 0.1113
Residuals 11  6.175  0.5614               
model <- with(dbook,PBIB.test(block, Genotype, replication, yield, k=3, method="VC"))

<<< to see the objects: means, comparison and groups. >>>
model$ANOVA
Analysis of Variance Table

Response: yield
                  Df  Sum Sq Mean Sq F value   Pr(>F)   
replication        1   0.600  0.6000  0.2983 0.595827   
Genotype.unadj    29 130.933  4.5149  2.2450 0.078789 . 
block/replication 18 171.278  9.5154  4.7315 0.005883 **
Residual          11  22.122  2.0111                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$groups
      yield.adj groups
gen10  7.719527      a
gen01  6.702668     ab
gen19  6.688105     ab
gen09  6.434092    abc
gen18  6.079660    abc
gen16  5.741100    abc
gen26  5.242943    abc
gen08  5.160284    abc
gen17  5.154956    abc
gen29  4.920606    abc
gen27  4.895090    abc
gen11  4.881068    abc
gen30  4.736661    abc
gen22  4.560904    abc
gen28  4.497487    abc
gen05  4.236467    abc
gen14  4.078535    abc
gen23  4.010469    abc
gen15  3.925524    abc
gen02  3.858485    abc
gen04  3.769153    abc
gen03  3.680560    abc
gen25  3.669765    abc
gen12  3.614243    abc
gen06  3.592020    abc
gen21  3.396933     bc
gen24  3.007228     bc
gen13  2.757585     bc
gen20  2.728381      c
gen07  2.259497      c
model
$ANOVA
Analysis of Variance Table

Response: yield
                  Df  Sum Sq Mean Sq F value   Pr(>F)   
replication        1   0.600  0.6000  0.2983 0.595827   
Genotype.unadj    29 130.933  4.5149  2.2450 0.078789 . 
block/replication 18 171.278  9.5154  4.7315 0.005883 **
Residual          11  22.122  2.0111                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$method
[1] "Variances component model"

$parameters
      test   name.t treatments blockSize blocks r alpha
  PBIB-lsd Genotype         30         3     10 2  0.05

$statistics
  Efficiency     Mean       CV
   0.6170213 4.533333 31.28236

$model

Call:
lm(formula = modelo)

Coefficients:
             (Intercept)              replication2              trt.adjgen02  
                 6.18553                   1.34091                  -2.04151  
            trt.adjgen03              trt.adjgen04              trt.adjgen05  
                -2.34498                  -3.16077                  -1.98708  
            trt.adjgen06              trt.adjgen07              trt.adjgen08  
                -2.97703                  -4.05598                  -1.21435  
            trt.adjgen09              trt.adjgen10              trt.adjgen11  
                -0.09151                   1.65407                  -0.97703  
            trt.adjgen12              trt.adjgen13              trt.adjgen14  
                -2.34211                  -3.38804                  -2.44151  
            trt.adjgen15              trt.adjgen16              trt.adjgen17  
                -1.89151                  -0.49474                  -1.08565  
            trt.adjgen18              trt.adjgen19              trt.adjgen20  
                -0.19151                  -0.29151                  -3.93301  
            trt.adjgen21              trt.adjgen22              trt.adjgen23  
                -3.13828                  -1.34151                  -2.61866  
            trt.adjgen24              trt.adjgen25              trt.adjgen26  
                -3.04737                  -2.09091                  -1.14151  
            trt.adjgen27              trt.adjgen28              trt.adjgen29  
                -1.49151                  -2.07225                  -1.55598  
            trt.adjgen30   replication1:block.adj2   replication2:block.adj2  
                -1.74151                   2.60957                        NA  
 replication1:block.adj3   replication2:block.adj3   replication1:block.adj4  
                 1.02656                        NA                   0.72895  
 replication2:block.adj4   replication1:block.adj5   replication2:block.adj5  
                      NA                  -2.09187                        NA  
 replication1:block.adj6   replication2:block.adj6   replication1:block.adj7  
                -0.75789                        NA                   4.02010  
 replication2:block.adj7   replication1:block.adj8   replication2:block.adj8  
                      NA                   1.29641                        NA  
 replication1:block.adj9   replication2:block.adj9  replication1:block.adj10  
                -1.82895                        NA                  -2.69306  
replication2:block.adj10  replication1:block.adj11  replication2:block.adj11  
                      NA                        NA                  -4.75789  
replication1:block.adj12  replication2:block.adj12  replication1:block.adj13  
                      NA                  -0.52536                        NA  
replication2:block.adj13  replication1:block.adj14  replication2:block.adj14  
                 0.26148                        NA                  -1.83708  
replication1:block.adj15  replication2:block.adj15  replication1:block.adj16  
                      NA                  -3.45550                        NA  
replication2:block.adj16  replication1:block.adj17  replication2:block.adj17  
                -3.74904                        NA                   0.22895  
replication1:block.adj18  replication2:block.adj18  replication1:block.adj19  
                      NA                   0.06411                        NA  
replication2:block.adj19  replication1:block.adj20  replication2:block.adj20  
                 0.67105                        NA                        NA  


$Fstat
    Fit Statistics
AIC       210.4067
BIC       315.1239

$comparison
                Difference   stderr pvalue
gen01 - gen02  2.844182738 1.994508 0.1816
gen01 - gen03  3.022107503 1.982955 0.1558
gen01 - gen04  2.933514780 1.826158 0.1364
gen01 - gen05  2.466200458 1.914426 0.2242
gen01 - gen06  3.110647497 1.914426 0.1324
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gen18 - gen24  3.072432259 1.945005 0.1424
gen18 - gen25  2.409894978 1.852361 0.2198
gen18 - gen26  0.836717099 1.975553 0.6800
gen18 - gen27  1.184570047 1.922628 0.5504
gen18 - gen28  1.582173847 1.994508 0.4444
gen18 - gen29  1.159054282 1.994508 0.5728
gen18 - gen30  1.342999377 1.975553 0.5106
gen19 - gen20  3.959724593 1.608895 0.0316
gen19 - gen21  3.291171887 1.852361 0.1032
gen19 - gen22  2.127200812 1.975553 0.3046
gen19 - gen23  2.677636335 1.945005 0.1960
gen19 - gen24  3.680877011 1.981614 0.0902
gen19 - gen25  3.018339729 1.994508 0.1584
gen19 - gen26  1.445161850 1.788631 0.4362
gen19 - gen27  1.793014799 1.922628 0.3710
gen19 - gen28  2.190618598 1.608895 0.2006
gen19 - gen29  1.767499033 1.852361 0.3604
gen19 - gen30  1.951444129 1.975553 0.3444
gen20 - gen21 -0.668552706 1.628410 0.6892
gen20 - gen22 -1.832523781 1.945005 0.3664
gen20 - gen23 -1.282088258 1.963311 0.5272
gen20 - gen24 -0.278847582 1.982955 0.8908
gen20 - gen25 -0.941384864 1.990728 0.6456
gen20 - gen26 -2.514562743 1.608895 0.1464
gen20 - gen27 -2.166709795 1.852361 0.2668
gen20 - gen28 -1.769105995 1.826158 0.3534
gen20 - gen29 -2.192225560 1.914426 0.2764
gen20 - gen30 -2.008280464 1.981614 0.3326
gen21 - gen22 -1.163971075 1.852361 0.5426
gen21 - gen23 -0.613535552 1.984825 0.7630
gen21 - gen24  0.389705123 1.989952 0.8484
gen21 - gen25 -0.272832158 1.984825 0.8932
gen21 - gen26 -1.846010037 1.608895 0.2756
gen21 - gen27 -1.498157089 1.608895 0.3718
gen21 - gen28 -1.100553289 1.914426 0.5770
gen21 - gen29 -1.523672854 1.963311 0.4540
gen21 - gen30 -1.339727759 1.994508 0.5156
gen22 - gen23  0.550435523 1.994508 0.7876
gen22 - gen24  1.553676199 1.981614 0.4496
gen22 - gen25  0.891138917 1.945005 0.6558
gen22 - gen26 -0.682038962 1.922628 0.7294
gen22 - gen27 -0.334186013 1.788631 0.8552
gen22 - gen28  0.063417786 1.981614 0.9750
gen22 - gen29 -0.359701779 1.994508 0.8602
gen22 - gen30 -0.175756683 1.995995 0.9314
gen23 - gen24  1.003240675 1.826158 0.5938
gen23 - gen25  0.340703394 1.875113 0.8592
gen23 - gen26 -1.232474485 1.981614 0.5466
gen23 - gen27 -0.884621537 1.994508 0.6660
gen23 - gen28 -0.487017737 1.875113 0.7998
gen23 - gen29 -0.910137302 1.628410 0.5874
gen23 - gen30 -0.726192206 1.608895 0.6604
gen24 - gen25 -0.662537281 1.826158 0.7236
gen24 - gen26 -2.235715160 1.994508 0.2862
gen24 - gen27 -1.887862212 1.994508 0.3642
gen24 - gen28 -1.490258412 1.963311 0.4638
gen24 - gen29 -1.913377977 1.914426 0.3390
gen24 - gen30 -1.729432882 1.608895 0.3054
gen25 - gen26 -1.573177879 1.994508 0.4470
gen25 - gen27 -1.225324931 1.981614 0.5490
gen25 - gen28 -0.827721131 1.982955 0.6844
gen25 - gen29 -1.250840696 1.955002 0.5354
gen25 - gen30 -1.066895600 1.852361 0.5762
gen26 - gen27  0.347852948 1.788631 0.8494
gen26 - gen28  0.745456748 1.852361 0.6950
gen26 - gen29  0.322337183 1.945005 0.8714
gen26 - gen30  0.506282279 1.995995 0.8044
gen27 - gen28  0.397603800 1.945005 0.8418
gen27 - gen29 -0.025515765 1.981614 0.9900
gen27 - gen30  0.158429330 2.001335 0.9384
gen28 - gen29 -0.423119565 1.628410 0.7998
gen28 - gen30 -0.239174470 1.945005 0.9044
gen29 - gen30  0.183945095 1.852361 0.9226

$means
      yield yield.adj       SE r       std Min Max  Q25 Q50  Q75
gen01   7.5  6.702668 1.418665 2 0.7071068   7   8 7.25 7.5 7.75
gen02   3.5  3.858485 1.424506 2 3.5355339   1   6 2.25 3.5 4.75
gen03   3.5  3.680560 1.418665 2 3.5355339   1   6 2.25 3.5 4.75
gen04   5.0  3.769153 1.418665 2 1.4142136   4   6 4.50 5.0 5.50
gen05   4.5  4.236467 1.418665 2 4.9497475   1   8 2.75 4.5 6.25
gen06   3.5  3.592020 1.418665 2 2.1213203   2   5 2.75 3.5 4.25
gen07   3.5  2.259497 1.418665 2 2.1213203   2   5 2.75 3.5 4.25
gen08   5.0  5.160284 1.418665 2 1.4142136   4   6 4.50 5.0 5.50
gen09   6.5  6.434092 1.424506 2 0.7071068   6   7 6.25 6.5 6.75
gen10   7.0  7.719527 1.418665 2 2.8284271   5   9 6.00 7.0 8.00
gen11   3.5  4.881068 1.418665 2 2.1213203   2   5 2.75 3.5 4.25
gen12   3.5  3.614243 1.418665 2 0.7071068   3   4 3.25 3.5 3.75
gen13   3.5  2.757585 1.418665 2 2.1213203   2   5 2.75 3.5 4.25
gen14   3.5  4.078535 1.424506 2 2.1213203   2   5 2.75 3.5 4.25
gen15   3.0  3.925524 1.424506 2 2.8284271   1   5 2.00 3.0 4.00
gen16   5.0  5.741100 1.418665 2 1.4142136   4   6 4.50 5.0 5.50
gen17   5.5  5.154956 1.418665 2 2.1213203   4   7 4.75 5.5 6.25
gen18   7.0  6.079660 1.424506 2 0.0000000   7   7 7.00 7.0 7.00
gen19   8.0  6.688105 1.424506 2 1.4142136   7   9 7.50 8.0 8.50
gen20   2.5  2.728381 1.418665 2 2.1213203   1   4 1.75 2.5 3.25
gen21   4.0  3.396933 1.418665 2 4.2426407   1   7 2.50 4.0 5.50
gen22   3.5  4.560904 1.424506 2 3.5355339   1   6 2.25 3.5 4.75
gen23   5.0  4.010469 1.418665 2 1.4142136   4   6 4.50 5.0 5.50
gen24   2.5  3.007228 1.418665 2 2.1213203   1   4 1.75 2.5 3.25
gen25   2.5  3.669765 1.418665 2 0.7071068   2   3 2.25 2.5 2.75
gen26   4.5  5.242943 1.424506 2 3.5355339   2   7 3.25 4.5 5.75
gen27   5.5  4.895090 1.424506 2 4.9497475   2   9 3.75 5.5 7.25
gen28   4.0  4.497487 1.418665 2 2.8284271   2   6 3.00 4.0 5.00
gen29   4.5  4.920606 1.418665 2 2.1213203   3   6 3.75 4.5 5.25
gen30   5.5  4.736661 1.424506 2 0.7071068   5   6 5.25 5.5 5.75

$groups
      yield.adj groups
gen10  7.719527      a
gen01  6.702668     ab
gen19  6.688105     ab
gen09  6.434092    abc
gen18  6.079660    abc
gen16  5.741100    abc
gen26  5.242943    abc
gen08  5.160284    abc
gen17  5.154956    abc
gen29  4.920606    abc
gen27  4.895090    abc
gen11  4.881068    abc
gen30  4.736661    abc
gen22  4.560904    abc
gen28  4.497487    abc
gen05  4.236467    abc
gen14  4.078535    abc
gen23  4.010469    abc
gen15  3.925524    abc
gen02  3.858485    abc
gen04  3.769153    abc
gen03  3.680560    abc
gen25  3.669765    abc
gen12  3.614243    abc
gen06  3.592020    abc
gen21  3.396933     bc
gen24  3.007228     bc
gen13  2.757585     bc
gen20  2.728381      c
gen07  2.259497      c

$vartau
            [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
 [1,] 2.01260952 0.03188288 0.04655440 0.34518357 0.18009671 0.18009671
 [2,] 0.03188288 2.02921724 0.72664106 0.03188288 0.12939052 0.05751596
 [3,] 0.04655440 0.72664106 2.01260952 0.03111061 0.18009671 0.04284445
 [4,] 0.34518357 0.03188288 0.03111061 2.01260952 0.10159224 0.68674950
 [5,] 0.18009671 0.12939052 0.18009671 0.10159224 2.01260952 0.04655440
 [6,] 0.18009671 0.05751596 0.04284445 0.68674950 0.04655440 2.01260952
 [7,] 0.10159224 0.30529201 0.68674950 0.04284445 0.34518357 0.03111061
 [8,] 0.08531425 0.12939052 0.08531425 0.25458582 0.03265515 0.68674950
 [9,] 0.12939052 0.07781324 0.05751596 0.30529201 0.03188288 0.72664106
[10,] 0.25458582 0.12939052 0.25458582 0.08531425 0.44622394 0.04284445
[11,] 0.08531425 0.30529201 0.34518357 0.04655440 0.68674950 0.03265515
[12,] 0.03111061 0.72664106 0.34518357 0.04655440 0.10159224 0.10159224
[13,] 0.04284445 0.72664106 0.44622394 0.03265515 0.25458582 0.04655440
[14,] 0.30529201 0.03721868 0.03188288 0.72664106 0.05751596 0.72664106
[15,] 0.03188288 0.42961621 0.30529201 0.05751596 0.05751596 0.12939052
[16,] 0.68674950 0.05751596 0.10159224 0.18009671 0.34518357 0.08531425
[17,] 0.04655440 0.30529201 0.25458582 0.08531425 0.04284445 0.18009671
[18,] 0.05751596 0.42961621 0.72664106 0.03188288 0.30529201 0.03188288
[19,] 0.72664106 0.02654707 0.03188288 0.72664106 0.12939052 0.30529201
[20,] 0.44622394 0.03188288 0.04284445 0.68674950 0.25458582 0.25458582
[21,] 0.34518357 0.05751596 0.08531425 0.25458582 0.68674950 0.10159224
[22,] 0.12939052 0.18096780 0.30529201 0.05751596 0.72664106 0.03188288
[23,] 0.10159224 0.12939052 0.10159224 0.18009671 0.03111061 0.34518357
[24,] 0.04284445 0.30529201 0.18009671 0.10159224 0.04655440 0.25458582
[25,] 0.03265515 0.72664106 0.68674950 0.04284445 0.08531425 0.08531425
[26,] 0.72664106 0.03721868 0.05751596 0.30529201 0.30529201 0.12939052
[27,] 0.30529201 0.07781324 0.12939052 0.12939052 0.72664106 0.05751596
[28,] 0.68674950 0.03188288 0.03265515 0.44622394 0.08531425 0.34518357
[29,] 0.25458582 0.05751596 0.04655440 0.34518357 0.04284445 0.44622394
[30,] 0.05751596 0.18096780 0.12939052 0.12939052 0.03188288 0.30529201
            [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
 [1,] 0.10159224 0.08531425 0.12939052 0.25458582 0.08531425 0.03111061
 [2,] 0.30529201 0.12939052 0.07781324 0.12939052 0.30529201 0.72664106
 [3,] 0.68674950 0.08531425 0.05751596 0.25458582 0.34518357 0.34518357
 [4,] 0.04284445 0.25458582 0.30529201 0.08531425 0.04655440 0.04655440
 [5,] 0.34518357 0.03265515 0.03188288 0.44622394 0.68674950 0.10159224
 [6,] 0.03111061 0.68674950 0.72664106 0.04284445 0.03265515 0.10159224
 [7,] 2.01260952 0.04284445 0.03188288 0.68674950 0.44622394 0.18009671
 [8,] 0.04284445 2.01260952 0.72664106 0.03111061 0.04655440 0.25458582
 [9,] 0.03188288 0.72664106 2.02921724 0.03188288 0.03188288 0.12939052
[10,] 0.68674950 0.03111061 0.03188288 2.01260952 0.34518357 0.08531425
[11,] 0.44622394 0.04655440 0.03188288 0.34518357 2.01260952 0.25458582
[12,] 0.18009671 0.25458582 0.12939052 0.08531425 0.25458582 2.01260952
[13,] 0.34518357 0.10159224 0.05751596 0.18009671 0.68674950 0.68674950
[14,] 0.03188288 0.30529201 0.42961621 0.05751596 0.03188288 0.05751596
[15,] 0.12939052 0.30529201 0.18096780 0.05751596 0.12939052 0.72664106
[16,] 0.25458582 0.04284445 0.05751596 0.68674950 0.18009671 0.04284445
[17,] 0.10159224 0.34518357 0.30529201 0.04655440 0.08531425 0.34518357
[18,] 0.72664106 0.05751596 0.03721868 0.30529201 0.72664106 0.30529201
[19,] 0.05751596 0.12939052 0.18096780 0.12939052 0.05751596 0.03188288
[20,] 0.08531425 0.10159224 0.12939052 0.18009671 0.10159224 0.03265515
[21,] 0.18009671 0.04655440 0.05751596 0.34518357 0.25458582 0.04655440
[22,] 0.72664106 0.03188288 0.02654707 0.72664106 0.72664106 0.12939052
[23,] 0.04655440 0.44622394 0.72664106 0.03265515 0.04284445 0.18009671
[24,] 0.08531425 0.68674950 0.30529201 0.04284445 0.10159224 0.68674950
[25,] 0.25458582 0.18009671 0.12939052 0.10159224 0.18009671 0.44622394
[26,] 0.12939052 0.05751596 0.07781324 0.30529201 0.12939052 0.03188288
[27,] 0.30529201 0.03188288 0.03721868 0.72664106 0.30529201 0.05751596
[28,] 0.04655440 0.18009671 0.30529201 0.10159224 0.04284445 0.04284445
[29,] 0.03265515 0.34518357 0.72664106 0.04655440 0.03111061 0.08531425
[30,] 0.05751596 0.72664106 0.42961621 0.03188288 0.05751596 0.30529201
           [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
 [1,] 0.04284445 0.30529201 0.03188288 0.68674950 0.04655440 0.05751596
 [2,] 0.72664106 0.03721868 0.42961621 0.05751596 0.30529201 0.42961621
 [3,] 0.44622394 0.03188288 0.30529201 0.10159224 0.25458582 0.72664106
 [4,] 0.03265515 0.72664106 0.05751596 0.18009671 0.08531425 0.03188288
 [5,] 0.25458582 0.05751596 0.05751596 0.34518357 0.04284445 0.30529201
 [6,] 0.04655440 0.72664106 0.12939052 0.08531425 0.18009671 0.03188288
 [7,] 0.34518357 0.03188288 0.12939052 0.25458582 0.10159224 0.72664106
 [8,] 0.10159224 0.30529201 0.30529201 0.04284445 0.34518357 0.05751596
 [9,] 0.05751596 0.42961621 0.18096780 0.05751596 0.30529201 0.03721868
[10,] 0.18009671 0.05751596 0.05751596 0.68674950 0.04655440 0.30529201
[11,] 0.68674950 0.03188288 0.12939052 0.18009671 0.08531425 0.72664106
[12,] 0.68674950 0.05751596 0.72664106 0.04284445 0.34518357 0.30529201
[13,] 2.01260952 0.03188288 0.30529201 0.08531425 0.18009671 0.72664106
[14,] 0.03188288 2.02921724 0.07781324 0.12939052 0.12939052 0.02654707
[15,] 0.30529201 0.07781324 2.02921724 0.03188288 0.72664106 0.18096780
[16,] 0.08531425 0.12939052 0.03188288 2.01260952 0.03265515 0.12939052
[17,] 0.18009671 0.12939052 0.72664106 0.03265515 2.01260952 0.12939052
[18,] 0.72664106 0.02654707 0.18096780 0.12939052 0.12939052 2.02921724
[19,] 0.03188288 0.42961621 0.03721868 0.30529201 0.05751596 0.03721868
[20,] 0.04655440 0.30529201 0.03188288 0.34518357 0.04284445 0.05751596
[21,] 0.10159224 0.12939052 0.03188288 0.44622394 0.03111061 0.12939052
[22,] 0.30529201 0.03721868 0.07781324 0.30529201 0.05751596 0.42961621
[23,] 0.08531425 0.30529201 0.30529201 0.04655440 0.68674950 0.05751596
[24,] 0.25458582 0.12939052 0.72664106 0.03111061 0.44622394 0.12939052
[25,] 0.34518357 0.05751596 0.72664106 0.04655440 0.68674950 0.30529201
[26,] 0.05751596 0.18096780 0.02654707 0.72664106 0.03188288 0.07781324
[27,] 0.12939052 0.07781324 0.03721868 0.72664106 0.03188288 0.18096780
[28,] 0.03111061 0.72664106 0.05751596 0.25458582 0.10159224 0.03188288
[29,] 0.04284445 0.72664106 0.12939052 0.10159224 0.25458582 0.03188288
[30,] 0.12939052 0.18096780 0.42961621 0.03188288 0.72664106 0.07781324
           [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
 [1,] 0.72664106 0.44622394 0.34518357 0.12939052 0.10159224 0.04284445
 [2,] 0.02654707 0.03188288 0.05751596 0.18096780 0.12939052 0.30529201
 [3,] 0.03188288 0.04284445 0.08531425 0.30529201 0.10159224 0.18009671
 [4,] 0.72664106 0.68674950 0.25458582 0.05751596 0.18009671 0.10159224
 [5,] 0.12939052 0.25458582 0.68674950 0.72664106 0.03111061 0.04655440
 [6,] 0.30529201 0.25458582 0.10159224 0.03188288 0.34518357 0.25458582
 [7,] 0.05751596 0.08531425 0.18009671 0.72664106 0.04655440 0.08531425
 [8,] 0.12939052 0.10159224 0.04655440 0.03188288 0.44622394 0.68674950
 [9,] 0.18096780 0.12939052 0.05751596 0.02654707 0.72664106 0.30529201
[10,] 0.12939052 0.18009671 0.34518357 0.72664106 0.03265515 0.04284445
[11,] 0.05751596 0.10159224 0.25458582 0.72664106 0.04284445 0.10159224
[12,] 0.03188288 0.03265515 0.04655440 0.12939052 0.18009671 0.68674950
[13,] 0.03188288 0.04655440 0.10159224 0.30529201 0.08531425 0.25458582
[14,] 0.42961621 0.30529201 0.12939052 0.03721868 0.30529201 0.12939052
[15,] 0.03721868 0.03188288 0.03188288 0.07781324 0.30529201 0.72664106
[16,] 0.30529201 0.34518357 0.44622394 0.30529201 0.04655440 0.03111061
[17,] 0.05751596 0.04284445 0.03111061 0.05751596 0.68674950 0.44622394
[18,] 0.03721868 0.05751596 0.12939052 0.42961621 0.05751596 0.12939052
[19,] 2.02921724 0.72664106 0.30529201 0.07781324 0.12939052 0.05751596
[20,] 0.72664106 2.01260952 0.68674950 0.12939052 0.08531425 0.04655440
[21,] 0.30529201 0.68674950 2.01260952 0.30529201 0.04284445 0.03265515
[22,] 0.07781324 0.12939052 0.30529201 2.02921724 0.03188288 0.05751596
[23,] 0.12939052 0.08531425 0.04284445 0.03188288 2.01260952 0.34518357
[24,] 0.05751596 0.04655440 0.03265515 0.05751596 0.34518357 2.01260952
[25,] 0.03188288 0.03111061 0.04284445 0.12939052 0.25458582 0.34518357
[26,] 0.42961621 0.72664106 0.72664106 0.18096780 0.05751596 0.03188288
[27,] 0.18096780 0.30529201 0.72664106 0.42961621 0.03188288 0.03188288
[28,] 0.72664106 0.34518357 0.18009671 0.05751596 0.25458582 0.08531425
[29,] 0.30529201 0.18009671 0.08531425 0.03188288 0.68674950 0.18009671
[30,] 0.07781324 0.05751596 0.03188288 0.03721868 0.72664106 0.72664106
           [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
 [1,] 0.03265515 0.72664106 0.30529201 0.68674950 0.25458582 0.05751596
 [2,] 0.72664106 0.03721868 0.07781324 0.03188288 0.05751596 0.18096780
 [3,] 0.68674950 0.05751596 0.12939052 0.03265515 0.04655440 0.12939052
 [4,] 0.04284445 0.30529201 0.12939052 0.44622394 0.34518357 0.12939052
 [5,] 0.08531425 0.30529201 0.72664106 0.08531425 0.04284445 0.03188288
 [6,] 0.08531425 0.12939052 0.05751596 0.34518357 0.44622394 0.30529201
 [7,] 0.25458582 0.12939052 0.30529201 0.04655440 0.03265515 0.05751596
 [8,] 0.18009671 0.05751596 0.03188288 0.18009671 0.34518357 0.72664106
 [9,] 0.12939052 0.07781324 0.03721868 0.30529201 0.72664106 0.42961621
[10,] 0.10159224 0.30529201 0.72664106 0.10159224 0.04655440 0.03188288
[11,] 0.18009671 0.12939052 0.30529201 0.04284445 0.03111061 0.05751596
[12,] 0.44622394 0.03188288 0.05751596 0.04284445 0.08531425 0.30529201
[13,] 0.34518357 0.05751596 0.12939052 0.03111061 0.04284445 0.12939052
[14,] 0.05751596 0.18096780 0.07781324 0.72664106 0.72664106 0.18096780
[15,] 0.72664106 0.02654707 0.03721868 0.05751596 0.12939052 0.42961621
[16,] 0.04655440 0.72664106 0.72664106 0.25458582 0.10159224 0.03188288
[17,] 0.68674950 0.03188288 0.03188288 0.10159224 0.25458582 0.72664106
[18,] 0.30529201 0.07781324 0.18096780 0.03188288 0.03188288 0.07781324
[19,] 0.03188288 0.42961621 0.18096780 0.72664106 0.30529201 0.07781324
[20,] 0.03111061 0.72664106 0.30529201 0.34518357 0.18009671 0.05751596
[21,] 0.04284445 0.72664106 0.72664106 0.18009671 0.08531425 0.03188288
[22,] 0.12939052 0.18096780 0.42961621 0.05751596 0.03188288 0.03721868
[23,] 0.25458582 0.05751596 0.03188288 0.25458582 0.68674950 0.72664106
[24,] 0.34518357 0.03188288 0.03188288 0.08531425 0.18009671 0.72664106
[25,] 2.01260952 0.03188288 0.05751596 0.04655440 0.10159224 0.30529201
[26,] 0.03188288 2.02921724 0.42961621 0.30529201 0.12939052 0.03721868
[27,] 0.05751596 0.42961621 2.02921724 0.12939052 0.05751596 0.02654707
[28,] 0.04655440 0.30529201 0.12939052 2.01260952 0.68674950 0.12939052
[29,] 0.10159224 0.12939052 0.05751596 0.68674950 2.01260952 0.30529201
[30,] 0.30529201 0.03721868 0.02654707 0.12939052 0.30529201 2.02921724

attr(,"class")
[1] "group"
plot(model,las=2)

Warning  values plot is not adjusted

Diseño latice

trt<-1:30
ntr<-length(trt)
r<-2
k<-3
s<-10
obs<-ntr*r
b <- s*r
book<-design.alpha(trt,k,r,seed=5)[[4]]

Alpha Design (0,1) - Serie  I 

Parameters Alpha Design
=======================
Treatmeans : 30
Block size : 3
Blocks     : 10
Replication: 2 

Efficiency factor
(E ) 0.6170213 

<<< Book >>>
# dataset
y<-c(5,2,7,6,4,9,7,6,7,9,6,2,1,1,3,2,4,6,7,9,8,7,6,4,3,2,2,1,1,2,
 1,1,2,4,5,6,7,8,6,5,4,3,1,1,2,5,4,2,7,6,6,5,6,4,5,7,6,5,5,4)
book<-data.frame(book,y=y)
rm(y,trt)
model <- with(book,PBIB.test(block, trt, replication, y, k=3, method="ML"))

<<< to see the objects: means, comparison and groups. >>>
model$ANOVA
Analysis of Variance Table

Response: y
          Df Sum Sq Mean Sq F value Pr(>F)
trt       29 32.669  1.1265  2.0066 0.1113
Residuals 11  6.175  0.5614               
model <- with(book,PBIB.test(block, trt, replication, y, k=3, method="VC"))

<<< to see the objects: means, comparison and groups. >>>
model$ANOVA
Analysis of Variance Table

Response: y
                  Df  Sum Sq Mean Sq F value   Pr(>F)   
replication        1   0.600  0.6000  0.2983 0.595827   
trt.unadj         29 130.933  4.5149  2.2450 0.078789 . 
block/replication 18 171.278  9.5154  4.7315 0.005883 **
Residual          11  22.122  2.0111                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model$groups
      y.adj groups
10 7.719527      a
1  6.702668     ab
19 6.688105     ab
9  6.434092    abc
18 6.079660    abc
16 5.741100    abc
26 5.242943    abc
8  5.160284    abc
17 5.154956    abc
29 4.920606    abc
27 4.895090    abc
11 4.881068    abc
30 4.736661    abc
22 4.560904    abc
28 4.497487    abc
5  4.236467    abc
14 4.078535    abc
23 4.010469    abc
15 3.925524    abc
2  3.858485    abc
4  3.769153    abc
3  3.680560    abc
25 3.669765    abc
12 3.614243    abc
6  3.592020    abc
21 3.396933     bc
24 3.007228     bc
13 2.757585     bc
20 2.728381      c
7  2.259497      c
model
$ANOVA
Analysis of Variance Table

Response: y
                  Df  Sum Sq Mean Sq F value   Pr(>F)   
replication        1   0.600  0.6000  0.2983 0.595827   
trt.unadj         29 130.933  4.5149  2.2450 0.078789 . 
block/replication 18 171.278  9.5154  4.7315 0.005883 **
Residual          11  22.122  2.0111                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

$method
[1] "Variances component model"

$parameters
      test name.t treatments blockSize blocks r alpha
  PBIB-lsd    trt         30         3     10 2  0.05

$statistics
  Efficiency     Mean       CV
   0.6170213 4.533333 31.28236

$model

Call:
lm(formula = modelo)

Coefficients:
             (Intercept)              replication2                  trt.adj2  
                 6.18553                   1.34091                  -2.04151  
                trt.adj3                  trt.adj4                  trt.adj5  
                -2.34498                  -3.16077                  -1.98708  
                trt.adj6                  trt.adj7                  trt.adj8  
                -2.97703                  -4.05598                  -1.21435  
                trt.adj9                 trt.adj10                 trt.adj11  
                -0.09151                   1.65407                  -0.97703  
               trt.adj12                 trt.adj13                 trt.adj14  
                -2.34211                  -3.38804                  -2.44151  
               trt.adj15                 trt.adj16                 trt.adj17  
                -1.89151                  -0.49474                  -1.08565  
               trt.adj18                 trt.adj19                 trt.adj20  
                -0.19151                  -0.29151                  -3.93301  
               trt.adj21                 trt.adj22                 trt.adj23  
                -3.13828                  -1.34151                  -2.61866  
               trt.adj24                 trt.adj25                 trt.adj26  
                -3.04737                  -2.09091                  -1.14151  
               trt.adj27                 trt.adj28                 trt.adj29  
                -1.49151                  -2.07225                  -1.55598  
               trt.adj30   replication1:block.adj2   replication2:block.adj2  
                -1.74151                   2.60957                        NA  
 replication1:block.adj3   replication2:block.adj3   replication1:block.adj4  
                 1.02656                        NA                   0.72895  
 replication2:block.adj4   replication1:block.adj5   replication2:block.adj5  
                      NA                  -2.09187                        NA  
 replication1:block.adj6   replication2:block.adj6   replication1:block.adj7  
                -0.75789                        NA                   4.02010  
 replication2:block.adj7   replication1:block.adj8   replication2:block.adj8  
                      NA                   1.29641                        NA  
 replication1:block.adj9   replication2:block.adj9  replication1:block.adj10  
                -1.82895                        NA                  -2.69306  
replication2:block.adj10  replication1:block.adj11  replication2:block.adj11  
                      NA                        NA                  -4.75789  
replication1:block.adj12  replication2:block.adj12  replication1:block.adj13  
                      NA                  -0.52536                        NA  
replication2:block.adj13  replication1:block.adj14  replication2:block.adj14  
                 0.26148                        NA                  -1.83708  
replication1:block.adj15  replication2:block.adj15  replication1:block.adj16  
                      NA                  -3.45550                        NA  
replication2:block.adj16  replication1:block.adj17  replication2:block.adj17  
                -3.74904                        NA                   0.22895  
replication1:block.adj18  replication2:block.adj18  replication1:block.adj19  
                      NA                   0.06411                        NA  
replication2:block.adj19  replication1:block.adj20  replication2:block.adj20  
                 0.67105                        NA                        NA  


$Fstat
    Fit Statistics
AIC       210.4067
BIC       315.1239

$comparison
          Difference   stderr pvalue
1 - 2    2.844182738 1.994508 0.1816
1 - 3    3.022107503 1.982955 0.1558
1 - 4    2.933514780 1.826158 0.1364
1 - 5    2.466200458 1.914426 0.2242
1 - 6    3.110647497 1.914426 0.1324
1 - 7    4.443170996 1.955002 0.0440
1 - 8    1.542383689 1.963311 0.4486
1 - 9    0.268575895 1.945005 0.8926
1 - 10  -1.016859362 1.875113 0.5984
1 - 11   1.821600053 1.963311 0.3734
1 - 12   3.088424622 1.990728 0.1490
1 - 13   3.945082729 1.984825 0.0724
1 - 14   2.624133378 1.852361 0.1842
1 - 15   2.777144357 1.994508 0.1914
1 - 16   0.961567504 1.628410 0.5668
1 - 17   1.547711475 1.982955 0.4516
1 - 18   0.623007494 1.981614 0.7592
1 - 19   0.014562743 1.608895 0.9930
1 - 20   3.974287336 1.769964 0.0462
1 - 21   3.305734630 1.826158 0.0976
1 - 22   2.141763555 1.945005 0.2944
1 - 23   2.692199078 1.955002 0.1958
1 - 24   3.695439754 1.984825 0.0896
1 - 25   3.032902472 1.989952 0.1558
1 - 26   1.459724593 1.608895 0.3838
1 - 27   1.807577541 1.852361 0.3502
1 - 28   2.205181341 1.628410 0.2028
1 - 29   1.782061776 1.875113 0.3624
1 - 30   1.966006872 1.981614 0.3424
2 - 3    0.177924765 1.608895 0.9140
2 - 4    0.089332042 1.994508 0.9650
2 - 5   -0.377982279 1.945005 0.8494
2 - 6    0.266464759 1.981614 0.8954
2 - 7    1.598988258 1.852361 0.4064
2 - 8   -1.301799049 1.945005 0.5172
2 - 9   -2.575606843 1.975553 0.2190
2 - 10  -3.861042100 1.945005 0.0726
2 - 11  -1.022582685 1.852361 0.5920
2 - 12   0.244241885 1.608895 0.8820
2 - 13   1.100899991 1.608895 0.5080
2 - 14  -0.220049360 1.995995 0.9142
2 - 15  -0.067038381 1.788631 0.9708
2 - 16  -1.882615234 1.981614 0.3624
2 - 17  -1.296471263 1.852361 0.4986
2 - 18  -2.221175244 1.788631 0.2402
2 - 19  -2.829619995 2.001335 0.1850
2 - 20   1.130104598 1.994508 0.5824
2 - 21   0.461551892 1.981614 0.8202
2 - 22  -0.702419183 1.922628 0.7218
2 - 23  -0.151983660 1.945005 0.9392
2 - 24   0.851257016 1.852361 0.6548
2 - 25   0.188719734 1.608895 0.9088
2 - 26  -1.384458145 1.995995 0.5024
2 - 27  -1.036605197 1.975553 0.6102
2 - 28  -0.639001397 1.994508 0.7546
2 - 29  -1.062120962 1.981614 0.6026
2 - 30  -0.878175866 1.922628 0.6568
3 - 4   -0.088592723 1.990728 0.9654
3 - 5   -0.555907045 1.914426 0.7770
3 - 6    0.088539994 1.984825 0.9652
3 - 7    1.421063493 1.628410 0.4014
3 - 8   -1.479723814 1.963311 0.4668
3 - 9   -2.753531608 1.981614 0.1922
3 - 10  -4.038966865 1.875113 0.0542
3 - 11  -1.200507450 1.826158 0.5244
3 - 12   0.066317119 1.826158 0.9716
3 - 13   0.922975226 1.769964 0.6124
3 - 14  -0.397974125 1.994508 0.8454
3 - 15  -0.244963146 1.852361 0.8972
3 - 16  -2.060539999 1.955002 0.3144
3 - 17  -1.474396028 1.875113 0.4484
3 - 18  -2.399100009 1.608895 0.1640
3 - 19  -3.007544760 1.994508 0.1598
3 - 20   0.952179833 1.984825 0.6408
3 - 21   0.283627127 1.963311 0.8878
3 - 22  -0.880343948 1.852361 0.6440
3 - 23  -0.329908425 1.955002 0.8690
3 - 24   0.673332250 1.914426 0.7316
3 - 25   0.010794969 1.628410 0.9948
3 - 26  -1.562382910 1.981614 0.4470
3 - 27  -1.214529962 1.945005 0.5450
3 - 28  -0.816926162 1.989952 0.6894
3 - 29  -1.240045727 1.982955 0.5444
3 - 30  -1.056100631 1.945005 0.5980
4 - 5   -0.467314321 1.955002 0.8154
4 - 6    0.177132717 1.628410 0.9154
4 - 7    1.509656216 1.984825 0.4628
4 - 8   -1.391131091 1.875113 0.4736
4 - 9   -2.664938885 1.852361 0.1780
4 - 10  -3.950374142 1.963311 0.0694
4 - 11  -1.111914727 1.982955 0.5862
4 - 12   0.154909843 1.982955 0.9392
4 - 13   1.011567949 1.989952 0.6212
4 - 14  -0.309381402 1.608895 0.8510
4 - 15  -0.156370423 1.981614 0.9386
4 - 16  -1.971947275 1.914426 0.3252
4 - 17  -1.385803305 1.963311 0.4950
4 - 18  -2.310507285 1.994508 0.2712
4 - 19  -2.918952037 1.608895 0.0970
4 - 20   1.040772556 1.628410 0.5358
4 - 21   0.372219851 1.875113 0.8462
4 - 22  -0.791751225 1.981614 0.6972
4 - 23  -0.241315701 1.914426 0.9020
4 - 24   0.761924974 1.955002 0.7042
4 - 25   0.099387692 1.984825 0.9610
4 - 26  -1.473790187 1.852361 0.4430
4 - 27  -1.125937238 1.945005 0.5744
4 - 28  -0.728333438 1.769964 0.6886
4 - 29  -1.151453003 1.826158 0.5412
4 - 30  -0.967507908 1.945005 0.6286
5 - 6    0.644447038 1.982955 0.7512
5 - 7    1.976970538 1.826158 0.3022
5 - 8   -0.923816770 1.989952 0.6516
5 - 9   -2.197624563 1.994508 0.2940
5 - 10  -3.483059821 1.769964 0.0748
5 - 11  -0.644600406 1.628410 0.6998
5 - 12   0.622224164 1.955002 0.7562
5 - 13   1.478882271 1.875113 0.4470
5 - 14   0.157932920 1.981614 0.9380
5 - 15   0.310943898 1.981614 0.8782
5 - 16  -1.504632954 1.826158 0.4274
5 - 17  -0.918488984 1.984825 0.6526
5 - 18  -1.843192964 1.852361 0.3410
5 - 19  -2.451637716 1.945005 0.2336
5 - 20   1.508086877 1.875113 0.4382
5 - 21   0.839534172 1.628410 0.6164
5 - 22  -0.324436904 1.608895 0.8438
5 - 23   0.225998620 1.990728 0.9116
5 - 24   1.229239295 1.982955 0.5480
5 - 25   0.566702014 1.963311 0.7782
5 - 26  -1.006475865 1.852361 0.5978
5 - 27  -0.658622917 1.608895 0.6902
5 - 28  -0.261019117 1.963311 0.8966
5 - 29  -0.684138682 1.984825 0.7368
5 - 30  -0.500193587 1.994508 0.8066
6 - 7    1.332523499 1.990728 0.5170
6 - 8   -1.568263808 1.628410 0.3562
6 - 9   -2.842071602 1.608895 0.1050
6 - 10  -4.127506859 1.984825 0.0618
6 - 11  -1.289047444 1.989952 0.5304
6 - 12  -0.022222874 1.955002 0.9912
6 - 13   0.834435232 1.982955 0.6820
6 - 14  -0.486514119 1.608895 0.7680
6 - 15  -0.333503140 1.945005 0.8670
6 - 16  -2.149079993 1.963311 0.2970
6 - 17  -1.562936022 1.914426 0.4316
6 - 18  -2.487640003 1.994508 0.2382
6 - 19  -3.096084754 1.852361 0.1228
6 - 20   0.863639839 1.875113 0.6540
6 - 21   0.195087133 1.955002 0.9224
6 - 22  -0.968883942 1.994508 0.6366
6 - 23  -0.418448419 1.826158 0.8230
6 - 24   0.584792257 1.875113 0.7610
6 - 25  -0.077745025 1.963311 0.9692
6 - 26  -1.650922904 1.945005 0.4140
6 - 27  -1.303069955 1.981614 0.5244
6 - 28  -0.905466156 1.826158 0.6298
6 - 29  -1.328585721 1.769964 0.4686
6 - 30  -1.144640625 1.852361 0.5492
7 - 8   -2.900787307 1.984825 0.1718
7 - 9   -4.174595101 1.994508 0.0604
7 - 10  -5.460030358 1.628410 0.0064
7 - 11  -2.621570943 1.769964 0.1666
7 - 12  -1.354746374 1.914426 0.4938
7 - 13  -0.498088267 1.826158 0.7900
7 - 14  -1.819037618 1.994508 0.3814
7 - 15  -1.666026639 1.945005 0.4100
7 - 16  -3.481603492 1.875113 0.0904
7 - 17  -2.895459521 1.955002 0.1666
7 - 18  -3.820163502 1.608895 0.0368
7 - 19  -4.428608253 1.981614 0.0472
7 - 20  -0.468883660 1.963311 0.8156
7 - 21  -1.137436366 1.914426 0.5644
7 - 22  -2.301407441 1.608895 0.1804
7 - 23  -1.750971918 1.982955 0.3962
7 - 24  -0.747731243 1.963311 0.7106
7 - 25  -1.410268524 1.875113 0.4678
7 - 26  -2.983446403 1.945005 0.1532
7 - 27  -2.635593455 1.852361 0.1826
7 - 28  -2.237989655 1.982955 0.2830
7 - 29  -2.661109220 1.989952 0.2082
7 - 30  -2.477164124 1.981614 0.2372
8 - 9   -1.273807794 1.608895 0.4452
8 - 10  -2.559243051 1.990728 0.2250
8 - 11   0.279216364 1.982955 0.8906
8 - 12   1.546040934 1.875113 0.4272
8 - 13   2.402699040 1.955002 0.2448
8 - 14   1.081749689 1.852361 0.5710
8 - 15   1.234760668 1.852361 0.5188
8 - 16  -0.580816184 1.984825 0.7752
8 - 17   0.005327786 1.826158 0.9978
8 - 18  -0.919376194 1.981614 0.6518
8 - 19  -1.527820946 1.945005 0.4488
8 - 20   2.431903647 1.955002 0.2394
8 - 21   1.763350942 1.982955 0.3928
8 - 22   0.599379866 1.994508 0.7694
8 - 23   1.149815390 1.769964 0.5292
8 - 24   2.153056065 1.628410 0.2130
8 - 25   1.490518784 1.914426 0.4526
8 - 26  -0.082659096 1.981614 0.9674
8 - 27   0.265193853 1.994508 0.8966
8 - 28   0.662797653 1.914426 0.7358
8 - 29   0.239678088 1.826158 0.8980
8 - 30   0.423623183 1.608895 0.7972
9 - 10  -1.285435257 1.994508 0.5324
9 - 11   1.553024158 1.994508 0.4526
9 - 12   2.819848727 1.945005 0.1750
9 - 13   3.676506834 1.981614 0.0906
9 - 14   2.355557483 1.788631 0.2146
9 - 15   2.508568462 1.922628 0.2186
9 - 16   0.692991609 1.981614 0.7332
9 - 17   1.279135580 1.852361 0.5042
9 - 18   0.354431599 1.995995 0.8622
9 - 19  -0.254013152 1.922628 0.8972
9 - 20   3.705711441 1.945005 0.0832
9 - 21   3.037158735 1.981614 0.1536
9 - 22   1.873187660 2.001335 0.3694
9 - 23   2.423623183 1.608895 0.1602
9 - 24   3.426863858 1.852361 0.0914
9 - 25   2.764326577 1.945005 0.1830
9 - 26   1.191148698 1.975553 0.5588
9 - 27   1.539001646 1.995995 0.4570
9 - 28   1.936605446 1.852361 0.3182
9 - 29   1.513485881 1.608895 0.3670
9 - 30   1.697430977 1.788631 0.3630
10 - 11  2.838459415 1.826158 0.1484
10 - 12  4.105283985 1.963311 0.0606
10 - 13  4.961942091 1.914426 0.0250
10 - 14  3.640992740 1.981614 0.0932
10 - 15  3.794003719 1.981614 0.0818
10 - 16  1.978426866 1.628410 0.2498
10 - 17  2.564570837 1.982955 0.2224
10 - 18  1.639866856 1.852361 0.3950
10 - 19  1.031422105 1.945005 0.6064
10 - 20  4.991146698 1.914426 0.0244
10 - 21  4.322593992 1.826158 0.0374
10 - 22  3.158622917 1.608895 0.0754
10 - 23  3.709058440 1.989952 0.0892
10 - 24  4.712299116 1.984825 0.0368
10 - 25  4.049761834 1.955002 0.0626
10 - 26  2.476583955 1.852361 0.2082
10 - 27  2.824436904 1.608895 0.1070
10 - 28  3.222040704 1.955002 0.1276
10 - 29  2.798921138 1.982955 0.1858
10 - 30  2.982866234 1.994508 0.1630
11 - 12  1.266824570 1.875113 0.5132
11 - 13  2.123482676 1.628410 0.2188
11 - 14  0.802533325 1.994508 0.6952
11 - 15  0.955544304 1.945005 0.6328
11 - 16 -0.860032549 1.914426 0.6620
11 - 17 -0.273888578 1.963311 0.8916
11 - 18 -1.198592559 1.608895 0.4720
11 - 19 -1.807037310 1.981614 0.3814
11 - 20  2.152687283 1.955002 0.2944
11 - 21  1.484134577 1.875113 0.4454
11 - 22  0.320163502 1.608895 0.8458
11 - 23  0.870599025 1.984825 0.6694
11 - 24  1.873839701 1.955002 0.3584
11 - 25  1.211302419 1.914426 0.5398
11 - 26 -0.361875460 1.945005 0.8558
11 - 27 -0.014022512 1.852361 0.9940
11 - 28  0.383581288 1.984825 0.8502
11 - 29 -0.039538277 1.990728 0.9846
11 - 30  0.144406819 1.981614 0.9432
12 - 13  0.856658107 1.628410 0.6092
12 - 14 -0.464291244 1.981614 0.8190
12 - 15 -0.311280266 1.608895 0.8502
12 - 16 -2.126857118 1.984825 0.3068
12 - 17 -1.540713148 1.826158 0.4168
12 - 18 -2.465417128 1.852361 0.2102
12 - 19 -3.073861880 1.994508 0.1516
12 - 20  0.885862713 1.989952 0.6648
12 - 21  0.217310008 1.982955 0.9148
12 - 22 -0.946661068 1.945005 0.6360
12 - 23 -0.396225544 1.914426 0.8398
12 - 24  0.607015131 1.628410 0.7164
12 - 25 -0.055522150 1.769964 0.9756
12 - 26 -1.628700029 1.994508 0.4314
12 - 27 -1.280847081 1.981614 0.5312
12 - 28 -0.883243281 1.984825 0.6650
12 - 29 -1.306362846 1.963311 0.5196
12 - 30 -1.122417751 1.852361 0.5568
13 - 14 -1.320949351 1.994508 0.5214
13 - 15 -1.167938372 1.852361 0.5412
13 - 16 -2.983515225 1.963311 0.1568
13 - 17 -2.397371254 1.914426 0.2364
13 - 18 -3.322075235 1.608895 0.0634
13 - 19 -3.930519986 1.994508 0.0744
13 - 20  0.029204607 1.982955 0.9886
13 - 21 -0.639348099 1.955002 0.7498
13 - 22 -1.803319174 1.852361 0.3512
13 - 23 -1.252883651 1.963311 0.5364
13 - 24 -0.249642975 1.875113 0.8964
13 - 25 -0.912180257 1.826158 0.6272
13 - 26 -2.485358136 1.981614 0.2358
13 - 27 -2.137505188 1.945005 0.2952
13 - 28 -1.739901388 1.990728 0.4008
13 - 29 -2.163020953 1.984825 0.2992
13 - 30 -1.979075857 1.945005 0.3308
14 - 15  0.153010979 1.975553 0.9396
14 - 16 -1.662565874 1.945005 0.4108
14 - 17 -1.076421903 1.945005 0.5910
14 - 18 -2.001125884 2.001335 0.3388
14 - 19 -2.609570635 1.788631 0.1726
14 - 20  1.350153958 1.852361 0.4814
14 - 21  0.681601252 1.945005 0.7326
14 - 22 -0.482369823 1.995995 0.8134
14 - 23  0.068065700 1.852361 0.9714
14 - 24  1.071306376 1.945005 0.5928
14 - 25  0.408769094 1.981614 0.8404
14 - 26 -1.164408785 1.922628 0.5570
14 - 27 -0.816555837 1.975553 0.6874
14 - 28 -0.418952037 1.608895 0.7994
14 - 29 -0.842071602 1.608895 0.6110
14 - 30 -0.658126506 1.922628 0.7386
15 - 16 -1.815576852 1.994508 0.3822
15 - 17 -1.229432882 1.608895 0.4608
15 - 18 -2.154136863 1.922628 0.2864
15 - 19 -2.762581614 1.995995 0.1938
15 - 20  1.197142979 1.994508 0.5606
15 - 21  0.528590274 1.994508 0.7958
15 - 22 -0.635380802 1.975553 0.7538
15 - 23 -0.084945279 1.852361 0.9642
15 - 24  0.918295397 1.608895 0.5796
15 - 25  0.255758115 1.608895 0.8766
15 - 26 -1.317419764 2.001335 0.5240
15 - 27 -0.969566815 1.995995 0.6366
15 - 28 -0.571963015 1.981614 0.7782
15 - 29 -0.995082580 1.945005 0.6190
15 - 30 -0.811137485 1.788631 0.6590
16 - 17  0.586143971 1.989952 0.7738
16 - 18 -0.338560010 1.945005 0.8650
16 - 19 -0.947004761 1.852361 0.6192
16 - 20  3.012719832 1.826158 0.1272
16 - 21  2.344167126 1.769964 0.2122
16 - 22  1.180196051 1.852361 0.5370
16 - 23  1.730631574 1.982955 0.4014
16 - 24  2.733872249 1.990728 0.1970
16 - 25  2.071334968 1.982955 0.3186
16 - 26  0.498157089 1.608895 0.7626
16 - 27  0.846010037 1.608895 0.6094
16 - 28  1.243613837 1.875113 0.5208
16 - 29  0.820494272 1.955002 0.6828
16 - 30  1.004439367 1.994508 0.6244
17 - 18 -0.924703981 1.945005 0.6438
17 - 19 -1.533148732 1.981614 0.4554
17 - 20  2.426575861 1.984825 0.2470
17 - 21  1.758023155 1.990728 0.3960
17 - 22  0.594052080 1.981614 0.7700
17 - 23  1.144487603 1.628410 0.4968
17 - 24  2.147728279 1.769964 0.2504
17 - 25  1.485190997 1.628410 0.3812
17 - 26 -0.087986882 1.994508 0.9656
17 - 27  0.259866067 1.994508 0.8986
17 - 28  0.657469866 1.955002 0.7430
17 - 29  0.234350301 1.875113 0.9028
17 - 30  0.418295397 1.608895 0.7996
18 - 19 -0.608444751 1.995995 0.7662
18 - 20  3.351279842 1.981614 0.1190
18 - 21  2.682727136 1.945005 0.1952
18 - 22  1.518756061 1.788631 0.4140
18 - 23  2.069191584 1.981614 0.3188
18 - 24  3.072432259 1.945005 0.1424
18 - 25  2.409894978 1.852361 0.2198
18 - 26  0.836717099 1.975553 0.6800
18 - 27  1.184570047 1.922628 0.5504
18 - 28  1.582173847 1.994508 0.4444
18 - 29  1.159054282 1.994508 0.5728
18 - 30  1.342999377 1.975553 0.5106
19 - 20  3.959724593 1.608895 0.0316
19 - 21  3.291171887 1.852361 0.1032
19 - 22  2.127200812 1.975553 0.3046
19 - 23  2.677636335 1.945005 0.1960
19 - 24  3.680877011 1.981614 0.0902
19 - 25  3.018339729 1.994508 0.1584
19 - 26  1.445161850 1.788631 0.4362
19 - 27  1.793014799 1.922628 0.3710
19 - 28  2.190618598 1.608895 0.2006
19 - 29  1.767499033 1.852361 0.3604
19 - 30  1.951444129 1.975553 0.3444
20 - 21 -0.668552706 1.628410 0.6892
20 - 22 -1.832523781 1.945005 0.3664
20 - 23 -1.282088258 1.963311 0.5272
20 - 24 -0.278847582 1.982955 0.8908
20 - 25 -0.941384864 1.990728 0.6456
20 - 26 -2.514562743 1.608895 0.1464
20 - 27 -2.166709795 1.852361 0.2668
20 - 28 -1.769105995 1.826158 0.3534
20 - 29 -2.192225560 1.914426 0.2764
20 - 30 -2.008280464 1.981614 0.3326
21 - 22 -1.163971075 1.852361 0.5426
21 - 23 -0.613535552 1.984825 0.7630
21 - 24  0.389705123 1.989952 0.8484
21 - 25 -0.272832158 1.984825 0.8932
21 - 26 -1.846010037 1.608895 0.2756
21 - 27 -1.498157089 1.608895 0.3718
21 - 28 -1.100553289 1.914426 0.5770
21 - 29 -1.523672854 1.963311 0.4540
21 - 30 -1.339727759 1.994508 0.5156
22 - 23  0.550435523 1.994508 0.7876
22 - 24  1.553676199 1.981614 0.4496
22 - 25  0.891138917 1.945005 0.6558
22 - 26 -0.682038962 1.922628 0.7294
22 - 27 -0.334186013 1.788631 0.8552
22 - 28  0.063417786 1.981614 0.9750
22 - 29 -0.359701779 1.994508 0.8602
22 - 30 -0.175756683 1.995995 0.9314
23 - 24  1.003240675 1.826158 0.5938
23 - 25  0.340703394 1.875113 0.8592
23 - 26 -1.232474485 1.981614 0.5466
23 - 27 -0.884621537 1.994508 0.6660
23 - 28 -0.487017737 1.875113 0.7998
23 - 29 -0.910137302 1.628410 0.5874
23 - 30 -0.726192206 1.608895 0.6604
24 - 25 -0.662537281 1.826158 0.7236
24 - 26 -2.235715160 1.994508 0.2862
24 - 27 -1.887862212 1.994508 0.3642
24 - 28 -1.490258412 1.963311 0.4638
24 - 29 -1.913377977 1.914426 0.3390
24 - 30 -1.729432882 1.608895 0.3054
25 - 26 -1.573177879 1.994508 0.4470
25 - 27 -1.225324931 1.981614 0.5490
25 - 28 -0.827721131 1.982955 0.6844
25 - 29 -1.250840696 1.955002 0.5354
25 - 30 -1.066895600 1.852361 0.5762
26 - 27  0.347852948 1.788631 0.8494
26 - 28  0.745456748 1.852361 0.6950
26 - 29  0.322337183 1.945005 0.8714
26 - 30  0.506282279 1.995995 0.8044
27 - 28  0.397603800 1.945005 0.8418
27 - 29 -0.025515765 1.981614 0.9900
27 - 30  0.158429330 2.001335 0.9384
28 - 29 -0.423119565 1.628410 0.7998
28 - 30 -0.239174470 1.945005 0.9044
29 - 30  0.183945095 1.852361 0.9226

$means
     y    y.adj       SE r       std Min Max  Q25 Q50  Q75
1  7.5 6.702668 1.418665 2 0.7071068   7   8 7.25 7.5 7.75
2  3.5 3.858485 1.424506 2 3.5355339   5   9 6.00 7.0 8.00
3  3.5 3.680560 1.418665 2 3.5355339   2   5 2.75 3.5 4.25
4  5.0 3.769153 1.418665 2 1.4142136   3   4 3.25 3.5 3.75
5  4.5 4.236467 1.418665 2 4.9497475   2   5 2.75 3.5 4.25
6  3.5 3.592020 1.418665 2 2.1213203   2   5 2.75 3.5 4.25
7  3.5 2.259497 1.418665 2 2.1213203   1   5 2.00 3.0 4.00
8  5.0 5.160284 1.418665 2 1.4142136   4   6 4.50 5.0 5.50
9  6.5 6.434092 1.424506 2 0.7071068   4   7 4.75 5.5 6.25
10 7.0 7.719527 1.418665 2 2.8284271   7   7 7.00 7.0 7.00
11 3.5 4.881068 1.418665 2 2.1213203   7   9 7.50 8.0 8.50
12 3.5 3.614243 1.418665 2 0.7071068   1   6 2.25 3.5 4.75
13 3.5 2.757585 1.418665 2 2.1213203   1   4 1.75 2.5 3.25
14 3.5 4.078535 1.424506 2 2.1213203   1   7 2.50 4.0 5.50
15 3.0 3.925524 1.424506 2 2.8284271   1   6 2.25 3.5 4.75
16 5.0 5.741100 1.418665 2 1.4142136   4   6 4.50 5.0 5.50
17 5.5 5.154956 1.418665 2 2.1213203   1   4 1.75 2.5 3.25
18 7.0 6.079660 1.424506 2 0.0000000   2   3 2.25 2.5 2.75
19 8.0 6.688105 1.424506 2 1.4142136   2   7 3.25 4.5 5.75
20 2.5 2.728381 1.418665 2 2.1213203   2   9 3.75 5.5 7.25
21 4.0 3.396933 1.418665 2 4.2426407   2   6 3.00 4.0 5.00
22 3.5 4.560904 1.424506 2 3.5355339   3   6 3.75 4.5 5.25
23 5.0 4.010469 1.418665 2 1.4142136   1   6 2.25 3.5 4.75
24 2.5 3.007228 1.418665 2 2.1213203   5   6 5.25 5.5 5.75
25 2.5 3.669765 1.418665 2 0.7071068   4   6 4.50 5.0 5.50
26 4.5 5.242943 1.424506 2 3.5355339   1   8 2.75 4.5 6.25
27 5.5 4.895090 1.424506 2 4.9497475   2   5 2.75 3.5 4.25
28 4.0 4.497487 1.418665 2 2.8284271   2   5 2.75 3.5 4.25
29 4.5 4.920606 1.418665 2 2.1213203   4   6 4.50 5.0 5.50
30 5.5 4.736661 1.424506 2 0.7071068   6   7 6.25 6.5 6.75

$groups
      y.adj groups
10 7.719527      a
1  6.702668     ab
19 6.688105     ab
9  6.434092    abc
18 6.079660    abc
16 5.741100    abc
26 5.242943    abc
8  5.160284    abc
17 5.154956    abc
29 4.920606    abc
27 4.895090    abc
11 4.881068    abc
30 4.736661    abc
22 4.560904    abc
28 4.497487    abc
5  4.236467    abc
14 4.078535    abc
23 4.010469    abc
15 3.925524    abc
2  3.858485    abc
4  3.769153    abc
3  3.680560    abc
25 3.669765    abc
12 3.614243    abc
6  3.592020    abc
21 3.396933     bc
24 3.007228     bc
13 2.757585     bc
20 2.728381      c
7  2.259497      c

$vartau
            [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
 [1,] 2.01260952 0.03188288 0.04655440 0.34518357 0.18009671 0.18009671
 [2,] 0.03188288 2.02921724 0.72664106 0.03188288 0.12939052 0.05751596
 [3,] 0.04655440 0.72664106 2.01260952 0.03111061 0.18009671 0.04284445
 [4,] 0.34518357 0.03188288 0.03111061 2.01260952 0.10159224 0.68674950
 [5,] 0.18009671 0.12939052 0.18009671 0.10159224 2.01260952 0.04655440
 [6,] 0.18009671 0.05751596 0.04284445 0.68674950 0.04655440 2.01260952
 [7,] 0.10159224 0.30529201 0.68674950 0.04284445 0.34518357 0.03111061
 [8,] 0.08531425 0.12939052 0.08531425 0.25458582 0.03265515 0.68674950
 [9,] 0.12939052 0.07781324 0.05751596 0.30529201 0.03188288 0.72664106
[10,] 0.25458582 0.12939052 0.25458582 0.08531425 0.44622394 0.04284445
[11,] 0.08531425 0.30529201 0.34518357 0.04655440 0.68674950 0.03265515
[12,] 0.03111061 0.72664106 0.34518357 0.04655440 0.10159224 0.10159224
[13,] 0.04284445 0.72664106 0.44622394 0.03265515 0.25458582 0.04655440
[14,] 0.30529201 0.03721868 0.03188288 0.72664106 0.05751596 0.72664106
[15,] 0.03188288 0.42961621 0.30529201 0.05751596 0.05751596 0.12939052
[16,] 0.68674950 0.05751596 0.10159224 0.18009671 0.34518357 0.08531425
[17,] 0.04655440 0.30529201 0.25458582 0.08531425 0.04284445 0.18009671
[18,] 0.05751596 0.42961621 0.72664106 0.03188288 0.30529201 0.03188288
[19,] 0.72664106 0.02654707 0.03188288 0.72664106 0.12939052 0.30529201
[20,] 0.44622394 0.03188288 0.04284445 0.68674950 0.25458582 0.25458582
[21,] 0.34518357 0.05751596 0.08531425 0.25458582 0.68674950 0.10159224
[22,] 0.12939052 0.18096780 0.30529201 0.05751596 0.72664106 0.03188288
[23,] 0.10159224 0.12939052 0.10159224 0.18009671 0.03111061 0.34518357
[24,] 0.04284445 0.30529201 0.18009671 0.10159224 0.04655440 0.25458582
[25,] 0.03265515 0.72664106 0.68674950 0.04284445 0.08531425 0.08531425
[26,] 0.72664106 0.03721868 0.05751596 0.30529201 0.30529201 0.12939052
[27,] 0.30529201 0.07781324 0.12939052 0.12939052 0.72664106 0.05751596
[28,] 0.68674950 0.03188288 0.03265515 0.44622394 0.08531425 0.34518357
[29,] 0.25458582 0.05751596 0.04655440 0.34518357 0.04284445 0.44622394
[30,] 0.05751596 0.18096780 0.12939052 0.12939052 0.03188288 0.30529201
            [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
 [1,] 0.10159224 0.08531425 0.12939052 0.25458582 0.08531425 0.03111061
 [2,] 0.30529201 0.12939052 0.07781324 0.12939052 0.30529201 0.72664106
 [3,] 0.68674950 0.08531425 0.05751596 0.25458582 0.34518357 0.34518357
 [4,] 0.04284445 0.25458582 0.30529201 0.08531425 0.04655440 0.04655440
 [5,] 0.34518357 0.03265515 0.03188288 0.44622394 0.68674950 0.10159224
 [6,] 0.03111061 0.68674950 0.72664106 0.04284445 0.03265515 0.10159224
 [7,] 2.01260952 0.04284445 0.03188288 0.68674950 0.44622394 0.18009671
 [8,] 0.04284445 2.01260952 0.72664106 0.03111061 0.04655440 0.25458582
 [9,] 0.03188288 0.72664106 2.02921724 0.03188288 0.03188288 0.12939052
[10,] 0.68674950 0.03111061 0.03188288 2.01260952 0.34518357 0.08531425
[11,] 0.44622394 0.04655440 0.03188288 0.34518357 2.01260952 0.25458582
[12,] 0.18009671 0.25458582 0.12939052 0.08531425 0.25458582 2.01260952
[13,] 0.34518357 0.10159224 0.05751596 0.18009671 0.68674950 0.68674950
[14,] 0.03188288 0.30529201 0.42961621 0.05751596 0.03188288 0.05751596
[15,] 0.12939052 0.30529201 0.18096780 0.05751596 0.12939052 0.72664106
[16,] 0.25458582 0.04284445 0.05751596 0.68674950 0.18009671 0.04284445
[17,] 0.10159224 0.34518357 0.30529201 0.04655440 0.08531425 0.34518357
[18,] 0.72664106 0.05751596 0.03721868 0.30529201 0.72664106 0.30529201
[19,] 0.05751596 0.12939052 0.18096780 0.12939052 0.05751596 0.03188288
[20,] 0.08531425 0.10159224 0.12939052 0.18009671 0.10159224 0.03265515
[21,] 0.18009671 0.04655440 0.05751596 0.34518357 0.25458582 0.04655440
[22,] 0.72664106 0.03188288 0.02654707 0.72664106 0.72664106 0.12939052
[23,] 0.04655440 0.44622394 0.72664106 0.03265515 0.04284445 0.18009671
[24,] 0.08531425 0.68674950 0.30529201 0.04284445 0.10159224 0.68674950
[25,] 0.25458582 0.18009671 0.12939052 0.10159224 0.18009671 0.44622394
[26,] 0.12939052 0.05751596 0.07781324 0.30529201 0.12939052 0.03188288
[27,] 0.30529201 0.03188288 0.03721868 0.72664106 0.30529201 0.05751596
[28,] 0.04655440 0.18009671 0.30529201 0.10159224 0.04284445 0.04284445
[29,] 0.03265515 0.34518357 0.72664106 0.04655440 0.03111061 0.08531425
[30,] 0.05751596 0.72664106 0.42961621 0.03188288 0.05751596 0.30529201
           [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
 [1,] 0.04284445 0.30529201 0.03188288 0.68674950 0.04655440 0.05751596
 [2,] 0.72664106 0.03721868 0.42961621 0.05751596 0.30529201 0.42961621
 [3,] 0.44622394 0.03188288 0.30529201 0.10159224 0.25458582 0.72664106
 [4,] 0.03265515 0.72664106 0.05751596 0.18009671 0.08531425 0.03188288
 [5,] 0.25458582 0.05751596 0.05751596 0.34518357 0.04284445 0.30529201
 [6,] 0.04655440 0.72664106 0.12939052 0.08531425 0.18009671 0.03188288
 [7,] 0.34518357 0.03188288 0.12939052 0.25458582 0.10159224 0.72664106
 [8,] 0.10159224 0.30529201 0.30529201 0.04284445 0.34518357 0.05751596
 [9,] 0.05751596 0.42961621 0.18096780 0.05751596 0.30529201 0.03721868
[10,] 0.18009671 0.05751596 0.05751596 0.68674950 0.04655440 0.30529201
[11,] 0.68674950 0.03188288 0.12939052 0.18009671 0.08531425 0.72664106
[12,] 0.68674950 0.05751596 0.72664106 0.04284445 0.34518357 0.30529201
[13,] 2.01260952 0.03188288 0.30529201 0.08531425 0.18009671 0.72664106
[14,] 0.03188288 2.02921724 0.07781324 0.12939052 0.12939052 0.02654707
[15,] 0.30529201 0.07781324 2.02921724 0.03188288 0.72664106 0.18096780
[16,] 0.08531425 0.12939052 0.03188288 2.01260952 0.03265515 0.12939052
[17,] 0.18009671 0.12939052 0.72664106 0.03265515 2.01260952 0.12939052
[18,] 0.72664106 0.02654707 0.18096780 0.12939052 0.12939052 2.02921724
[19,] 0.03188288 0.42961621 0.03721868 0.30529201 0.05751596 0.03721868
[20,] 0.04655440 0.30529201 0.03188288 0.34518357 0.04284445 0.05751596
[21,] 0.10159224 0.12939052 0.03188288 0.44622394 0.03111061 0.12939052
[22,] 0.30529201 0.03721868 0.07781324 0.30529201 0.05751596 0.42961621
[23,] 0.08531425 0.30529201 0.30529201 0.04655440 0.68674950 0.05751596
[24,] 0.25458582 0.12939052 0.72664106 0.03111061 0.44622394 0.12939052
[25,] 0.34518357 0.05751596 0.72664106 0.04655440 0.68674950 0.30529201
[26,] 0.05751596 0.18096780 0.02654707 0.72664106 0.03188288 0.07781324
[27,] 0.12939052 0.07781324 0.03721868 0.72664106 0.03188288 0.18096780
[28,] 0.03111061 0.72664106 0.05751596 0.25458582 0.10159224 0.03188288
[29,] 0.04284445 0.72664106 0.12939052 0.10159224 0.25458582 0.03188288
[30,] 0.12939052 0.18096780 0.42961621 0.03188288 0.72664106 0.07781324
           [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
 [1,] 0.72664106 0.44622394 0.34518357 0.12939052 0.10159224 0.04284445
 [2,] 0.02654707 0.03188288 0.05751596 0.18096780 0.12939052 0.30529201
 [3,] 0.03188288 0.04284445 0.08531425 0.30529201 0.10159224 0.18009671
 [4,] 0.72664106 0.68674950 0.25458582 0.05751596 0.18009671 0.10159224
 [5,] 0.12939052 0.25458582 0.68674950 0.72664106 0.03111061 0.04655440
 [6,] 0.30529201 0.25458582 0.10159224 0.03188288 0.34518357 0.25458582
 [7,] 0.05751596 0.08531425 0.18009671 0.72664106 0.04655440 0.08531425
 [8,] 0.12939052 0.10159224 0.04655440 0.03188288 0.44622394 0.68674950
 [9,] 0.18096780 0.12939052 0.05751596 0.02654707 0.72664106 0.30529201
[10,] 0.12939052 0.18009671 0.34518357 0.72664106 0.03265515 0.04284445
[11,] 0.05751596 0.10159224 0.25458582 0.72664106 0.04284445 0.10159224
[12,] 0.03188288 0.03265515 0.04655440 0.12939052 0.18009671 0.68674950
[13,] 0.03188288 0.04655440 0.10159224 0.30529201 0.08531425 0.25458582
[14,] 0.42961621 0.30529201 0.12939052 0.03721868 0.30529201 0.12939052
[15,] 0.03721868 0.03188288 0.03188288 0.07781324 0.30529201 0.72664106
[16,] 0.30529201 0.34518357 0.44622394 0.30529201 0.04655440 0.03111061
[17,] 0.05751596 0.04284445 0.03111061 0.05751596 0.68674950 0.44622394
[18,] 0.03721868 0.05751596 0.12939052 0.42961621 0.05751596 0.12939052
[19,] 2.02921724 0.72664106 0.30529201 0.07781324 0.12939052 0.05751596
[20,] 0.72664106 2.01260952 0.68674950 0.12939052 0.08531425 0.04655440
[21,] 0.30529201 0.68674950 2.01260952 0.30529201 0.04284445 0.03265515
[22,] 0.07781324 0.12939052 0.30529201 2.02921724 0.03188288 0.05751596
[23,] 0.12939052 0.08531425 0.04284445 0.03188288 2.01260952 0.34518357
[24,] 0.05751596 0.04655440 0.03265515 0.05751596 0.34518357 2.01260952
[25,] 0.03188288 0.03111061 0.04284445 0.12939052 0.25458582 0.34518357
[26,] 0.42961621 0.72664106 0.72664106 0.18096780 0.05751596 0.03188288
[27,] 0.18096780 0.30529201 0.72664106 0.42961621 0.03188288 0.03188288
[28,] 0.72664106 0.34518357 0.18009671 0.05751596 0.25458582 0.08531425
[29,] 0.30529201 0.18009671 0.08531425 0.03188288 0.68674950 0.18009671
[30,] 0.07781324 0.05751596 0.03188288 0.03721868 0.72664106 0.72664106
           [,25]      [,26]      [,27]      [,28]      [,29]      [,30]
 [1,] 0.03265515 0.72664106 0.30529201 0.68674950 0.25458582 0.05751596
 [2,] 0.72664106 0.03721868 0.07781324 0.03188288 0.05751596 0.18096780
 [3,] 0.68674950 0.05751596 0.12939052 0.03265515 0.04655440 0.12939052
 [4,] 0.04284445 0.30529201 0.12939052 0.44622394 0.34518357 0.12939052
 [5,] 0.08531425 0.30529201 0.72664106 0.08531425 0.04284445 0.03188288
 [6,] 0.08531425 0.12939052 0.05751596 0.34518357 0.44622394 0.30529201
 [7,] 0.25458582 0.12939052 0.30529201 0.04655440 0.03265515 0.05751596
 [8,] 0.18009671 0.05751596 0.03188288 0.18009671 0.34518357 0.72664106
 [9,] 0.12939052 0.07781324 0.03721868 0.30529201 0.72664106 0.42961621
[10,] 0.10159224 0.30529201 0.72664106 0.10159224 0.04655440 0.03188288
[11,] 0.18009671 0.12939052 0.30529201 0.04284445 0.03111061 0.05751596
[12,] 0.44622394 0.03188288 0.05751596 0.04284445 0.08531425 0.30529201
[13,] 0.34518357 0.05751596 0.12939052 0.03111061 0.04284445 0.12939052
[14,] 0.05751596 0.18096780 0.07781324 0.72664106 0.72664106 0.18096780
[15,] 0.72664106 0.02654707 0.03721868 0.05751596 0.12939052 0.42961621
[16,] 0.04655440 0.72664106 0.72664106 0.25458582 0.10159224 0.03188288
[17,] 0.68674950 0.03188288 0.03188288 0.10159224 0.25458582 0.72664106
[18,] 0.30529201 0.07781324 0.18096780 0.03188288 0.03188288 0.07781324
[19,] 0.03188288 0.42961621 0.18096780 0.72664106 0.30529201 0.07781324
[20,] 0.03111061 0.72664106 0.30529201 0.34518357 0.18009671 0.05751596
[21,] 0.04284445 0.72664106 0.72664106 0.18009671 0.08531425 0.03188288
[22,] 0.12939052 0.18096780 0.42961621 0.05751596 0.03188288 0.03721868
[23,] 0.25458582 0.05751596 0.03188288 0.25458582 0.68674950 0.72664106
[24,] 0.34518357 0.03188288 0.03188288 0.08531425 0.18009671 0.72664106
[25,] 2.01260952 0.03188288 0.05751596 0.04655440 0.10159224 0.30529201
[26,] 0.03188288 2.02921724 0.42961621 0.30529201 0.12939052 0.03721868
[27,] 0.05751596 0.42961621 2.02921724 0.12939052 0.05751596 0.02654707
[28,] 0.04655440 0.30529201 0.12939052 2.01260952 0.68674950 0.12939052
[29,] 0.10159224 0.12939052 0.05751596 0.68674950 2.01260952 0.30529201
[30,] 0.30529201 0.03721868 0.02654707 0.12939052 0.30529201 2.02921724

attr(,"class")
[1] "group"
plot(model,las=2)

Warning  values plot is not adjusted